I am done

rl/Lib/site-packages/sympy/physics/quantum/tests/test_anticommutator.py

@@ -0,0 +1,56 @@
+from sympy.core.numbers import Integer
+from sympy.core.symbol import symbols
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.anticommutator import AntiCommutator as AComm
+from sympy.physics.quantum.operator import Operator
+
+
+a, b, c = symbols('a,b,c')
+A, B, C, D = symbols('A,B,C,D', commutative=False)
+
+
+def test_anticommutator():
+    ac = AComm(A, B)
+    assert isinstance(ac, AComm)
+    assert ac.is_commutative is False
+    assert ac.subs(A, C) == AComm(C, B)
+
+
+def test_commutator_identities():
+    assert AComm(a*A, b*B) == a*b*AComm(A, B)
+    assert AComm(A, A) == 2*A**2
+    assert AComm(A, B) == AComm(B, A)
+    assert AComm(a, b) == 2*a*b
+    assert AComm(A, B).doit() == A*B + B*A
+
+
+def test_anticommutator_dagger():
+    assert Dagger(AComm(A, B)) == AComm(Dagger(A), Dagger(B))
+
+
+class Foo(Operator):
+
+    def _eval_anticommutator_Bar(self, bar):
+        return Integer(0)
+
+
+class Bar(Operator):
+    pass
+
+
+class Tam(Operator):
+
+    def _eval_anticommutator_Foo(self, foo):
+        return Integer(1)
+
+
+def test_eval_commutator():
+    F = Foo('F')
+    B = Bar('B')
+    T = Tam('T')
+    assert AComm(F, B).doit() == 0
+    assert AComm(B, F).doit() == 0
+    assert AComm(F, T).doit() == 1
+    assert AComm(T, F).doit() == 1
+    assert AComm(B, T).doit() == B*T + T*B

rl/Lib/site-packages/sympy/physics/quantum/tests/test_boson.py

@@ -0,0 +1,50 @@
+from math import prod
+
+from sympy.core.numbers import Rational
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum import Dagger, Commutator, qapply
+from sympy.physics.quantum.boson import BosonOp
+from sympy.physics.quantum.boson import (
+    BosonFockKet, BosonFockBra, BosonCoherentKet, BosonCoherentBra)
+
+
+def test_bosonoperator():
+    a = BosonOp('a')
+    b = BosonOp('b')
+
+    assert isinstance(a, BosonOp)
+    assert isinstance(Dagger(a), BosonOp)
+
+    assert a.is_annihilation
+    assert not Dagger(a).is_annihilation
+
+    assert BosonOp("a") == BosonOp("a", True)
+    assert BosonOp("a") != BosonOp("c")
+    assert BosonOp("a", True) != BosonOp("a", False)
+
+    assert Commutator(a, Dagger(a)).doit() == 1
+
+    assert Commutator(a, Dagger(b)).doit() == a * Dagger(b) - Dagger(b) * a
+
+    assert Dagger(exp(a)) == exp(Dagger(a))
+
+
+def test_boson_states():
+    a = BosonOp("a")
+
+    # Fock states
+    n = 3
+    assert (BosonFockBra(0) * BosonFockKet(1)).doit() == 0
+    assert (BosonFockBra(1) * BosonFockKet(1)).doit() == 1
+    assert qapply(BosonFockBra(n) * Dagger(a)**n * BosonFockKet(0)) \
+        == sqrt(prod(range(1, n+1)))
+
+    # Coherent states
+    alpha1, alpha2 = 1.2, 4.3
+    assert (BosonCoherentBra(alpha1) * BosonCoherentKet(alpha1)).doit() == 1
+    assert (BosonCoherentBra(alpha2) * BosonCoherentKet(alpha2)).doit() == 1
+    assert abs((BosonCoherentBra(alpha1) * BosonCoherentKet(alpha2)).doit() -
+               exp((alpha1 - alpha2) ** 2 * Rational(-1, 2))) < 1e-12
+    assert qapply(a * BosonCoherentKet(alpha1)) == \
+        alpha1 * BosonCoherentKet(alpha1)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_cartesian.py

@@ -0,0 +1,104 @@
+"""Tests for cartesian.py"""
+
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.delta_functions import DiracDelta
+from sympy.sets.sets import Interval
+
+from sympy.physics.quantum import qapply, represent, L2, Dagger
+from sympy.physics.quantum import Commutator, hbar
+from sympy.physics.quantum.cartesian import (
+    XOp, YOp, ZOp, PxOp, X, Y, Z, Px, XKet, XBra, PxKet, PxBra,
+    PositionKet3D, PositionBra3D
+)
+from sympy.physics.quantum.operator import DifferentialOperator
+
+x, y, z, x_1, x_2, x_3, y_1, z_1 = symbols('x,y,z,x_1,x_2,x_3,y_1,z_1')
+px, py, px_1, px_2 = symbols('px py px_1 px_2')
+
+
+def test_x():
+    assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert Commutator(X, Px).doit() == I*hbar
+    assert qapply(X*XKet(x)) == x*XKet(x)
+    assert XKet(x).dual_class() == XBra
+    assert XBra(x).dual_class() == XKet
+    assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x - y)
+    assert (PxBra(px)*XKet(x)).doit() == \
+        exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
+    assert represent(XKet(x)) == DiracDelta(x - x_1)
+    assert represent(XBra(x)) == DiracDelta(-x + x_1)
+    assert XBra(x).position == x
+    assert represent(XOp()*XKet()) == x*DiracDelta(x - x_2)
+    assert represent(XOp()*XKet()*XBra('y')) == \
+        x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
+    assert represent(XBra("y")*XKet()) == DiracDelta(x - y)
+    assert represent(
+        XKet()*XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x)
+
+    rep_p = represent(XOp(), basis=PxOp)
+    assert rep_p == hbar*I*DiracDelta(px_1 - px_2)*DifferentialOperator(px_1)
+    assert rep_p == represent(XOp(), basis=PxOp())
+    assert rep_p == represent(XOp(), basis=PxKet)
+    assert rep_p == represent(XOp(), basis=PxKet())
+
+    assert represent(XOp()*PxKet(), basis=PxKet) == \
+        hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px)
+
+
+def test_p():
+    assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert qapply(Px*PxKet(px)) == px*PxKet(px)
+    assert PxKet(px).dual_class() == PxBra
+    assert PxBra(x).dual_class() == PxKet
+    assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px - py)
+    assert (XBra(x)*PxKet(px)).doit() == \
+        exp(I*x*px/hbar)/sqrt(2*pi*hbar)
+    assert represent(PxKet(px)) == DiracDelta(px - px_1)
+
+    rep_x = represent(PxOp(), basis=XOp)
+    assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1)
+    assert rep_x == represent(PxOp(), basis=XOp())
+    assert rep_x == represent(PxOp(), basis=XKet)
+    assert rep_x == represent(PxOp(), basis=XKet())
+
+    assert represent(PxOp()*XKet(), basis=XKet) == \
+        -hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x)
+    assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \
+        -hbar*I*DiracDelta(x - y)*DifferentialOperator(x)
+
+
+def test_3dpos():
+    assert Y.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert Z.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    test_ket = PositionKet3D(x, y, z)
+    assert qapply(X*test_ket) == x*test_ket
+    assert qapply(Y*test_ket) == y*test_ket
+    assert qapply(Z*test_ket) == z*test_ket
+    assert qapply(X*Y*test_ket) == x*y*test_ket
+    assert qapply(X*Y*Z*test_ket) == x*y*z*test_ket
+    assert qapply(Y*Z*test_ket) == y*z*test_ket
+
+    assert PositionKet3D() == test_ket
+    assert YOp() == Y
+    assert ZOp() == Z
+
+    assert PositionKet3D.dual_class() == PositionBra3D
+    assert PositionBra3D.dual_class() == PositionKet3D
+
+    other_ket = PositionKet3D(x_1, y_1, z_1)
+    assert (Dagger(other_ket)*test_ket).doit() == \
+        DiracDelta(x - x_1)*DiracDelta(y - y_1)*DiracDelta(z - z_1)
+
+    assert test_ket.position_x == x
+    assert test_ket.position_y == y
+    assert test_ket.position_z == z
+    assert other_ket.position_x == x_1
+    assert other_ket.position_y == y_1
+    assert other_ket.position_z == z_1
+
+    # TODO: Add tests for representations

rl/Lib/site-packages/sympy/physics/quantum/tests/test_cg.py

@@ -0,0 +1,183 @@
+from sympy.concrete.summations import Sum
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum.cg import Wigner3j, Wigner6j, Wigner9j, CG, cg_simp
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+
+def test_cg_simp_add():
+    j, m1, m1p, m2, m2p = symbols('j m1 m1p m2 m2p')
+    # Test Varshalovich 8.7.1 Eq 1
+    a = CG(S.Half, S.Half, 0, 0, S.Half, S.Half)
+    b = CG(S.Half, Rational(-1, 2), 0, 0, S.Half, Rational(-1, 2))
+    c = CG(1, 1, 0, 0, 1, 1)
+    d = CG(1, 0, 0, 0, 1, 0)
+    e = CG(1, -1, 0, 0, 1, -1)
+    assert cg_simp(a + b) == 2
+    assert cg_simp(c + d + e) == 3
+    assert cg_simp(a + b + c + d + e) == 5
+    assert cg_simp(a + b + c) == 2 + c
+    assert cg_simp(2*a + b) == 2 + a
+    assert cg_simp(2*c + d + e) == 3 + c
+    assert cg_simp(5*a + 5*b) == 10
+    assert cg_simp(5*c + 5*d + 5*e) == 15
+    assert cg_simp(-a - b) == -2
+    assert cg_simp(-c - d - e) == -3
+    assert cg_simp(-6*a - 6*b) == -12
+    assert cg_simp(-4*c - 4*d - 4*e) == -12
+    a = CG(S.Half, S.Half, j, 0, S.Half, S.Half)
+    b = CG(S.Half, Rational(-1, 2), j, 0, S.Half, Rational(-1, 2))
+    c = CG(1, 1, j, 0, 1, 1)
+    d = CG(1, 0, j, 0, 1, 0)
+    e = CG(1, -1, j, 0, 1, -1)
+    assert cg_simp(a + b) == 2*KroneckerDelta(j, 0)
+    assert cg_simp(c + d + e) == 3*KroneckerDelta(j, 0)
+    assert cg_simp(a + b + c + d + e) == 5*KroneckerDelta(j, 0)
+    assert cg_simp(a + b + c) == 2*KroneckerDelta(j, 0) + c
+    assert cg_simp(2*a + b) == 2*KroneckerDelta(j, 0) + a
+    assert cg_simp(2*c + d + e) == 3*KroneckerDelta(j, 0) + c
+    assert cg_simp(5*a + 5*b) == 10*KroneckerDelta(j, 0)
+    assert cg_simp(5*c + 5*d + 5*e) == 15*KroneckerDelta(j, 0)
+    assert cg_simp(-a - b) == -2*KroneckerDelta(j, 0)
+    assert cg_simp(-c - d - e) == -3*KroneckerDelta(j, 0)
+    assert cg_simp(-6*a - 6*b) == -12*KroneckerDelta(j, 0)
+    assert cg_simp(-4*c - 4*d - 4*e) == -12*KroneckerDelta(j, 0)
+    # Test Varshalovich 8.7.1 Eq 2
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 0, 0)
+    b = CG(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0)
+    c = CG(1, 1, 1, -1, 0, 0)
+    d = CG(1, 0, 1, 0, 0, 0)
+    e = CG(1, -1, 1, 1, 0, 0)
+    assert cg_simp(a - b) == sqrt(2)
+    assert cg_simp(c - d + e) == sqrt(3)
+    assert cg_simp(a - b + c - d + e) == sqrt(2) + sqrt(3)
+    assert cg_simp(a - b + c) == sqrt(2) + c
+    assert cg_simp(2*a - b) == sqrt(2) + a
+    assert cg_simp(2*c - d + e) == sqrt(3) + c
+    assert cg_simp(5*a - 5*b) == 5*sqrt(2)
+    assert cg_simp(5*c - 5*d + 5*e) == 5*sqrt(3)
+    assert cg_simp(-a + b) == -sqrt(2)
+    assert cg_simp(-c + d - e) == -sqrt(3)
+    assert cg_simp(-6*a + 6*b) == -6*sqrt(2)
+    assert cg_simp(-4*c + 4*d - 4*e) == -4*sqrt(3)
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), j, 0)
+    b = CG(S.Half, Rational(-1, 2), S.Half, S.Half, j, 0)
+    c = CG(1, 1, 1, -1, j, 0)
+    d = CG(1, 0, 1, 0, j, 0)
+    e = CG(1, -1, 1, 1, j, 0)
+    assert cg_simp(a - b) == sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(c - d + e) == sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(a - b + c - d + e) == sqrt(
+        2)*KroneckerDelta(j, 0) + sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(a - b + c) == sqrt(2)*KroneckerDelta(j, 0) + c
+    assert cg_simp(2*a - b) == sqrt(2)*KroneckerDelta(j, 0) + a
+    assert cg_simp(2*c - d + e) == sqrt(3)*KroneckerDelta(j, 0) + c
+    assert cg_simp(5*a - 5*b) == 5*sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(5*c - 5*d + 5*e) == 5*sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(-a + b) == -sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(-c + d - e) == -sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(-6*a + 6*b) == -6*sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(-4*c + 4*d - 4*e) == -4*sqrt(3)*KroneckerDelta(j, 0)
+    # Test Varshalovich 8.7.2 Eq 9
+    # alpha=alphap,beta=betap case
+    # numerical
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 1, 0)**2
+    b = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 0, 0)**2
+    c = CG(1, 0, 1, 1, 1, 1)**2
+    d = CG(1, 0, 1, 1, 2, 1)**2
+    assert cg_simp(a + b) == 1
+    assert cg_simp(c + d) == 1
+    assert cg_simp(a + b + c + d) == 2
+    assert cg_simp(4*a + 4*b) == 4
+    assert cg_simp(4*c + 4*d) == 4
+    assert cg_simp(5*a + 3*b) == 3 + 2*a
+    assert cg_simp(5*c + 3*d) == 3 + 2*c
+    assert cg_simp(-a - b) == -1
+    assert cg_simp(-c - d) == -1
+    # symbolic
+    a = CG(S.Half, m1, S.Half, m2, 1, 1)**2
+    b = CG(S.Half, m1, S.Half, m2, 1, 0)**2
+    c = CG(S.Half, m1, S.Half, m2, 1, -1)**2
+    d = CG(S.Half, m1, S.Half, m2, 0, 0)**2
+    assert cg_simp(a + b + c + d) == 1
+    assert cg_simp(4*a + 4*b + 4*c + 4*d) == 4
+    assert cg_simp(3*a + 5*b + 3*c + 4*d) == 3 + 2*b + d
+    assert cg_simp(-a - b - c - d) == -1
+    a = CG(1, m1, 1, m2, 2, 2)**2
+    b = CG(1, m1, 1, m2, 2, 1)**2
+    c = CG(1, m1, 1, m2, 2, 0)**2
+    d = CG(1, m1, 1, m2, 2, -1)**2
+    e = CG(1, m1, 1, m2, 2, -2)**2
+    f = CG(1, m1, 1, m2, 1, 1)**2
+    g = CG(1, m1, 1, m2, 1, 0)**2
+    h = CG(1, m1, 1, m2, 1, -1)**2
+    i = CG(1, m1, 1, m2, 0, 0)**2
+    assert cg_simp(a + b + c + d + e + f + g + h + i) == 1
+    assert cg_simp(4*(a + b + c + d + e + f + g + h + i)) == 4
+    assert cg_simp(a + b + 2*c + d + 4*e + f + g + h + i) == 1 + c + 3*e
+    assert cg_simp(-a - b - c - d - e - f - g - h - i) == -1
+    # alpha!=alphap or beta!=betap case
+    # numerical
+    a = CG(S.Half, S(
+        1)/2, S.Half, Rational(-1, 2), 1, 0)*CG(S.Half, Rational(-1, 2), S.Half, S.Half, 1, 0)
+    b = CG(S.Half, S(
+        1)/2, S.Half, Rational(-1, 2), 0, 0)*CG(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0)
+    c = CG(1, 1, 1, 0, 2, 1)*CG(1, 0, 1, 1, 2, 1)
+    d = CG(1, 1, 1, 0, 1, 1)*CG(1, 0, 1, 1, 1, 1)
+    assert cg_simp(a + b) == 0
+    assert cg_simp(c + d) == 0
+    # symbolic
+    a = CG(S.Half, m1, S.Half, m2, 1, 1)*CG(S.Half, m1p, S.Half, m2p, 1, 1)
+    b = CG(S.Half, m1, S.Half, m2, 1, 0)*CG(S.Half, m1p, S.Half, m2p, 1, 0)
+    c = CG(S.Half, m1, S.Half, m2, 1, -1)*CG(S.Half, m1p, S.Half, m2p, 1, -1)
+    d = CG(S.Half, m1, S.Half, m2, 0, 0)*CG(S.Half, m1p, S.Half, m2p, 0, 0)
+    assert cg_simp(a + b + c + d) == KroneckerDelta(m1, m1p)*KroneckerDelta(m2, m2p)
+    a = CG(1, m1, 1, m2, 2, 2)*CG(1, m1p, 1, m2p, 2, 2)
+    b = CG(1, m1, 1, m2, 2, 1)*CG(1, m1p, 1, m2p, 2, 1)
+    c = CG(1, m1, 1, m2, 2, 0)*CG(1, m1p, 1, m2p, 2, 0)
+    d = CG(1, m1, 1, m2, 2, -1)*CG(1, m1p, 1, m2p, 2, -1)
+    e = CG(1, m1, 1, m2, 2, -2)*CG(1, m1p, 1, m2p, 2, -2)
+    f = CG(1, m1, 1, m2, 1, 1)*CG(1, m1p, 1, m2p, 1, 1)
+    g = CG(1, m1, 1, m2, 1, 0)*CG(1, m1p, 1, m2p, 1, 0)
+    h = CG(1, m1, 1, m2, 1, -1)*CG(1, m1p, 1, m2p, 1, -1)
+    i = CG(1, m1, 1, m2, 0, 0)*CG(1, m1p, 1, m2p, 0, 0)
+    assert cg_simp(
+        a + b + c + d + e + f + g + h + i) == KroneckerDelta(m1, m1p)*KroneckerDelta(m2, m2p)
+
+
+def test_cg_simp_sum():
+    x, a, b, c, cp, alpha, beta, gamma, gammap = symbols(
+        'x a b c cp alpha beta gamma gammap')
+    # Varshalovich 8.7.1 Eq 1
+    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)
+                   )) == x*(2*a + 1)*KroneckerDelta(b, 0)
+    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)) + CG(1, 0, 1, 0, 1, 0)) == x*(2*a + 1)*KroneckerDelta(b, 0) + CG(1, 0, 1, 0, 1, 0)
+    assert cg_simp(2 * Sum(CG(1, alpha, 0, 0, 1, alpha), (alpha, -1, 1))) == 6
+    # Varshalovich 8.7.1 Eq 2
+    assert cg_simp(x*Sum((-1)**(a - alpha) * CG(a, alpha, a, -alpha, c,
+                   0), (alpha, -a, a))) == x*sqrt(2*a + 1)*KroneckerDelta(c, 0)
+    assert cg_simp(3*Sum((-1)**(2 - alpha) * CG(
+        2, alpha, 2, -alpha, 0, 0), (alpha, -2, 2))) == 3*sqrt(5)
+    # Varshalovich 8.7.2 Eq 4
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)*KroneckerDelta(gamma, gammap)
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, c, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(gamma, gammap)
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gamma), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)
+    assert cg_simp(Sum(CG(
+        a, alpha, b, beta, c, gamma)**2, (alpha, -a, a), (beta, -b, b))) == 1
+    assert cg_simp(Sum(CG(2, alpha, 1, beta, 2, gamma)*CG(2, alpha, 1, beta, 2, gammap), (alpha, -2, 2), (beta, -1, 1))) == KroneckerDelta(gamma, gammap)
+
+
+def test_doit():
+    assert Wigner3j(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0).doit() == -sqrt(2)/2
+    assert Wigner3j(1/2,1/2,1/2,1/2,1/2,1/2).doit() == 0
+    assert Wigner3j(9/2,9/2,9/2,9/2,9/2,9/2).doit() ==  0
+    assert Wigner6j(1, 2, 3, 2, 1, 2).doit() == sqrt(21)/105
+    assert Wigner6j(3, 1, 2, 2, 2, 1).doit() == sqrt(21) / 105
+    assert Wigner9j(
+        2, 1, 1, Rational(3, 2), S.Half, 1, S.Half, S.Half, 0).doit() == sqrt(2)/12
+    assert CG(S.Half, S.Half, S.Half, Rational(-1, 2), 1, 0).doit() == sqrt(2)/2
+    # J minus M is not integer
+    assert Wigner3j(1, -1, S.Half, S.Half, 1, S.Half).doit() == 0
+    assert CG(4, -1, S.Half, S.Half, 4, Rational(-1, 2)).doit() == 0

rl/Lib/site-packages/sympy/physics/quantum/tests/test_circuitplot.py

@@ -0,0 +1,69 @@
+from sympy.physics.quantum.circuitplot import labeller, render_label, Mz, CreateOneQubitGate,\
+     CreateCGate
+from sympy.physics.quantum.gate import CNOT, H, SWAP, CGate, S, T
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+mpl = import_module('matplotlib')
+
+def test_render_label():
+    assert render_label('q0') == r'$\left|q0\right\rangle$'
+    assert render_label('q0', {'q0': '0'}) == r'$\left|q0\right\rangle=\left|0\right\rangle$'
+
+def test_Mz():
+    assert str(Mz(0)) == 'Mz(0)'
+
+def test_create1():
+    Qgate = CreateOneQubitGate('Q')
+    assert str(Qgate(0)) == 'Q(0)'
+
+def test_createc():
+    Qgate = CreateCGate('Q')
+    assert str(Qgate([1],0)) == 'C((1),Q(0))'
+
+def test_labeller():
+    """Test the labeller utility"""
+    assert labeller(2) == ['q_1', 'q_0']
+    assert labeller(3,'j') == ['j_2', 'j_1', 'j_0']
+
+def test_cnot():
+    """Test a simple cnot circuit. Right now this only makes sure the code doesn't
+    raise an exception, and some simple properties
+    """
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(CNOT(1,0),2,labels=labeller(2))
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == ['q_1', 'q_0']
+
+    c = CircuitPlot(CNOT(1,0),2)
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == []
+
+def test_ex1():
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(CNOT(1,0)*H(1),2,labels=labeller(2))
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == ['q_1', 'q_0']
+
+def test_ex4():
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(SWAP(0,2)*H(0)* CGate((0,),S(1)) *H(1)*CGate((0,),T(2))\
+                    *CGate((1,),S(2))*H(2),3,labels=labeller(3,'j'))
+    assert c.ngates == 7
+    assert c.nqubits == 3
+    assert c.labels == ['j_2', 'j_1', 'j_0']

rl/Lib/site-packages/sympy/physics/quantum/tests/test_circuitutils.py

@@ -0,0 +1,402 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.core.symbol import Symbol
+from sympy.utilities import numbered_symbols
+from sympy.physics.quantum.gate import X, Y, Z, H, CNOT, CGate
+from sympy.physics.quantum.identitysearch import bfs_identity_search
+from sympy.physics.quantum.circuitutils import (kmp_table, find_subcircuit,
+        replace_subcircuit, convert_to_symbolic_indices,
+        convert_to_real_indices, random_reduce, random_insert,
+        flatten_ids)
+from sympy.testing.pytest import slow
+
+
+def create_gate_sequence(qubit=0):
+    gates = (X(qubit), Y(qubit), Z(qubit), H(qubit))
+    return gates
+
+
+def test_kmp_table():
+    word = ('a', 'b', 'c', 'd', 'a', 'b', 'd')
+    expected_table = [-1, 0, 0, 0, 0, 1, 2]
+    assert expected_table == kmp_table(word)
+
+    word = ('P', 'A', 'R', 'T', 'I', 'C', 'I', 'P', 'A', 'T', 'E', ' ',
+            'I', 'N', ' ', 'P', 'A', 'R', 'A', 'C', 'H', 'U', 'T', 'E')
+    expected_table = [-1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0,
+                      0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0]
+    assert expected_table == kmp_table(word)
+
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    word = (x, y, y, x, z)
+    expected_table = [-1, 0, 0, 0, 1]
+    assert expected_table == kmp_table(word)
+
+    word = (x, x, y, h, z)
+    expected_table = [-1, 0, 1, 0, 0]
+    assert expected_table == kmp_table(word)
+
+
+def test_find_subcircuit():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    x1 = X(1)
+    y1 = Y(1)
+
+    i0 = Symbol('i0')
+    x_i0 = X(i0)
+    y_i0 = Y(i0)
+    z_i0 = Z(i0)
+    h_i0 = H(i0)
+
+    circuit = (x, y, z)
+
+    assert find_subcircuit(circuit, (x,)) == 0
+    assert find_subcircuit(circuit, (x1,)) == -1
+    assert find_subcircuit(circuit, (y,)) == 1
+    assert find_subcircuit(circuit, (h,)) == -1
+    assert find_subcircuit(circuit, Mul(x, h)) == -1
+    assert find_subcircuit(circuit, Mul(x, y, z)) == 0
+    assert find_subcircuit(circuit, Mul(y, z)) == 1
+    assert find_subcircuit(Mul(*circuit), (x, y, z, h)) == -1
+    assert find_subcircuit(Mul(*circuit), (z, y, x)) == -1
+    assert find_subcircuit(circuit, (x,), start=2, end=1) == -1
+
+    circuit = (x, y, x, y, z)
+    assert find_subcircuit(Mul(*circuit), Mul(x, y, z)) == 2
+    assert find_subcircuit(circuit, (x,), start=1) == 2
+    assert find_subcircuit(circuit, (x, y), start=1, end=2) == -1
+    assert find_subcircuit(Mul(*circuit), (x, y), start=1, end=3) == -1
+    assert find_subcircuit(circuit, (x, y), start=1, end=4) == 2
+    assert find_subcircuit(circuit, (x, y), start=2, end=4) == 2
+
+    circuit = (x, y, z, x1, x, y, z, h, x, y, x1,
+               x, y, z, h, y1, h)
+    assert find_subcircuit(circuit, (x, y, z, h, y1)) == 11
+
+    circuit = (x, y, x_i0, y_i0, z_i0, z)
+    assert find_subcircuit(circuit, (x_i0, y_i0, z_i0)) == 2
+
+    circuit = (x_i0, y_i0, z_i0, x_i0, y_i0, h_i0)
+    subcircuit = (x_i0, y_i0, z_i0)
+    result = find_subcircuit(circuit, subcircuit)
+    assert result == 0
+
+
+def test_replace_subcircuit():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    # Standard cases
+    circuit = (z, y, x, x)
+    remove = (z, y, x)
+    assert replace_subcircuit(circuit, Mul(*remove)) == (x,)
+    assert replace_subcircuit(circuit, remove + (x,)) == ()
+    assert replace_subcircuit(circuit, remove, pos=1) == circuit
+    assert replace_subcircuit(circuit, remove, pos=0) == (x,)
+    assert replace_subcircuit(circuit, (x, x), pos=2) == (z, y)
+    assert replace_subcircuit(circuit, (h,)) == circuit
+
+    circuit = (x, y, x, y, z)
+    remove = (x, y, z)
+    assert replace_subcircuit(Mul(*circuit), Mul(*remove)) == (x, y)
+    remove = (x, y, x, y)
+    assert replace_subcircuit(circuit, remove) == (z,)
+
+    circuit = (x, h, cgate_z, h, cnot)
+    remove = (x, h, cgate_z)
+    assert replace_subcircuit(circuit, Mul(*remove), pos=-1) == (h, cnot)
+    assert replace_subcircuit(circuit, remove, pos=1) == circuit
+    remove = (h, h)
+    assert replace_subcircuit(circuit, remove) == circuit
+    remove = (h, cgate_z, h, cnot)
+    assert replace_subcircuit(circuit, remove) == (x,)
+
+    replace = (h, x)
+    actual = replace_subcircuit(circuit, remove,
+                     replace=replace)
+    assert actual == (x, h, x)
+
+    circuit = (x, y, h, x, y, z)
+    remove = (x, y)
+    replace = (cnot, cgate_z)
+    actual = replace_subcircuit(circuit, remove,
+                     replace=Mul(*replace))
+    assert actual == (cnot, cgate_z, h, x, y, z)
+
+    actual = replace_subcircuit(circuit, remove,
+                     replace=replace, pos=1)
+    assert actual == (x, y, h, cnot, cgate_z, z)
+
+
+def test_convert_to_symbolic_indices():
+    (x, y, z, h) = create_gate_sequence()
+
+    i0 = Symbol('i0')
+    exp_map = {i0: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x,))
+    assert actual == (X(i0),)
+    assert act_map == exp_map
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0))
+    exp_map = {i0: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x, y, z, h))
+    assert actual == expected
+    assert exp_map == act_map
+
+    (x1, y1, z1, h1) = create_gate_sequence(1)
+    i1 = Symbol('i1')
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0))
+    exp_map = {i0: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x1, y1, z1, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0), X(i1), Y(i1), Z(i1), H(i1))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x, y, z, h,
+                                         x1, y1, z1, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(Mul(x1, y1,
+                                         z1, h1, x, y, z, h))
+    assert actual == expected
+    assert act_map == exp_map
+
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1), H(i0), H(i1))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(Mul(x, x1,
+                                         y, y1, z, z1, h, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x1, x, y1, y,
+                                         z1, z, h1, h))
+    assert actual == expected
+    assert act_map == exp_map
+
+    cnot_10 = CNOT(1, 0)
+    cnot_01 = CNOT(0, 1)
+    cgate_z_10 = CGate(1, Z(0))
+    cgate_z_01 = CGate(0, Z(1))
+
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1),
+                H(i0), H(i1), CNOT(i1, i0), CNOT(i0, i1),
+                CGate(i1, Z(i0)), CGate(i0, Z(i1)))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    args = (x, x1, y, y1, z, z1, h, h1, cnot_10, cnot_01,
+            cgate_z_10, cgate_z_01)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (x1, x, y1, y, z1, z, h1, h, cnot_10, cnot_01,
+            cgate_z_10, cgate_z_01)
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1),
+                H(i0), H(i1), CNOT(i0, i1), CNOT(i1, i0),
+                CGate(i0, Z(i1)), CGate(i1, Z(i0)))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_10, h, cgate_z_01, h)
+    expected = (CNOT(i0, i1), H(i1), CGate(i1, Z(i0)), H(i1))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_01, h1, cgate_z_10, h1)
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_10, h1, cgate_z_01, h1)
+    expected = (CNOT(i0, i1), H(i0), CGate(i1, Z(i0)), H(i0))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    i2 = Symbol('i2')
+    ccgate_z = CGate(0, CGate(1, Z(2)))
+    ccgate_x = CGate(1, CGate(2, X(0)))
+    args = (ccgate_z, ccgate_x)
+
+    expected = (CGate(i0, CGate(i1, Z(i2))), CGate(i1, CGate(i2, X(i0))))
+    exp_map = {i0: Integer(0), i1: Integer(1), i2: Integer(2)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    ndx_map = {i0: Integer(0)}
+    index_gen = numbered_symbols(prefix='i', start=1)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args,
+                                         qubit_map=ndx_map,
+                                         start=i0,
+                                         gen=index_gen)
+    assert actual == expected
+    assert act_map == exp_map
+
+    i3 = Symbol('i3')
+    cgate_x0_c321 = CGate((3, 2, 1), X(0))
+    exp_map = {i0: Integer(3), i1: Integer(2),
+               i2: Integer(1), i3: Integer(0)}
+    expected = (CGate((i0, i1, i2), X(i3)),)
+    args = (cgate_x0_c321,)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+
+def test_convert_to_real_indices():
+    i0 = Symbol('i0')
+    i1 = Symbol('i1')
+
+    (x, y, z, h) = create_gate_sequence()
+
+    x_i0 = X(i0)
+    y_i0 = Y(i0)
+    z_i0 = Z(i0)
+
+    qubit_map = {i0: 0}
+    args = (z_i0, y_i0, x_i0)
+    expected = (z, y, x)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    cnot_10 = CNOT(1, 0)
+    cnot_01 = CNOT(0, 1)
+    cgate_z_10 = CGate(1, Z(0))
+    cgate_z_01 = CGate(0, Z(1))
+
+    cnot_i1_i0 = CNOT(i1, i0)
+    cnot_i0_i1 = CNOT(i0, i1)
+    cgate_z_i1_i0 = CGate(i1, Z(i0))
+
+    qubit_map = {i0: 0, i1: 1}
+    args = (cnot_i1_i0,)
+    expected = (cnot_10,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    args = (cgate_z_i1_i0,)
+    expected = (cgate_z_10,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    args = (cnot_i0_i1,)
+    expected = (cnot_01,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    qubit_map = {i0: 1, i1: 0}
+    args = (cgate_z_i1_i0,)
+    expected = (cgate_z_01,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    i2 = Symbol('i2')
+    ccgate_z = CGate(i0, CGate(i1, Z(i2)))
+    ccgate_x = CGate(i1, CGate(i2, X(i0)))
+
+    qubit_map = {i0: 0, i1: 1, i2: 2}
+    args = (ccgate_z, ccgate_x)
+    expected = (CGate(0, CGate(1, Z(2))), CGate(1, CGate(2, X(0))))
+    actual = convert_to_real_indices(Mul(*args), qubit_map)
+    assert actual == expected
+
+    qubit_map = {i0: 1, i2: 0, i1: 2}
+    args = (ccgate_x, ccgate_z)
+    expected = (CGate(2, CGate(0, X(1))), CGate(1, CGate(2, Z(0))))
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+
+@slow
+def test_random_reduce():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    gate_list = [x, y, z]
+    ids = list(bfs_identity_search(gate_list, 1, max_depth=4))
+
+    circuit = (x, y, h, z, cnot)
+    assert random_reduce(circuit, []) == circuit
+    assert random_reduce(circuit, ids) == circuit
+
+    seq = [2, 11, 9, 3, 5]
+    circuit = (x, y, z, x, y, h)
+    assert random_reduce(circuit, ids, seed=seq) == (x, y, h)
+
+    circuit = (x, x, y, y, z, z)
+    assert random_reduce(circuit, ids, seed=seq) == (x, x, y, y)
+
+    seq = [14, 13, 0]
+    assert random_reduce(circuit, ids, seed=seq) == (y, y, z, z)
+
+    gate_list = [x, y, z, h, cnot, cgate_z]
+    ids = list(bfs_identity_search(gate_list, 2, max_depth=4))
+
+    seq = [25]
+    circuit = (x, y, z, y, h, y, h, cgate_z, h, cnot)
+    expected = (x, y, z, cgate_z, h, cnot)
+    assert random_reduce(circuit, ids, seed=seq) == expected
+    circuit = Mul(*circuit)
+    assert random_reduce(circuit, ids, seed=seq) == expected
+
+
+@slow
+def test_random_insert():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    choices = [(x, x)]
+    circuit = (y, y)
+    loc, choice = 0, 0
+    actual = random_insert(circuit, choices, seed=[loc, choice])
+    assert actual == (x, x, y, y)
+
+    circuit = (x, y, z, h)
+    choices = [(h, h), (x, y, z)]
+    expected = (x, x, y, z, y, z, h)
+    loc, choice = 1, 1
+    actual = random_insert(circuit, choices, seed=[loc, choice])
+    assert actual == expected
+
+    gate_list = [x, y, z, h, cnot, cgate_z]
+    ids = list(bfs_identity_search(gate_list, 2, max_depth=4))
+
+    eq_ids = flatten_ids(ids)
+
+    circuit = (x, y, h, cnot, cgate_z)
+    expected = (x, z, x, z, x, y, h, cnot, cgate_z)
+    loc, choice = 1, 30
+    actual = random_insert(circuit, eq_ids, seed=[loc, choice])
+    assert actual == expected
+    circuit = Mul(*circuit)
+    actual = random_insert(circuit, eq_ids, seed=[loc, choice])
+    assert actual == expected

rl/Lib/site-packages/sympy/physics/quantum/tests/test_commutator.py

@@ -0,0 +1,81 @@
+from sympy.core.numbers import Integer
+from sympy.core.symbol import symbols
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.commutator import Commutator as Comm
+from sympy.physics.quantum.operator import Operator
+
+
+a, b, c = symbols('a,b,c')
+n = symbols('n', integer=True)
+A, B, C, D = symbols('A,B,C,D', commutative=False)
+
+
+def test_commutator():
+    c = Comm(A, B)
+    assert c.is_commutative is False
+    assert isinstance(c, Comm)
+    assert c.subs(A, C) == Comm(C, B)
+
+
+def test_commutator_identities():
+    assert Comm(a*A, b*B) == a*b*Comm(A, B)
+    assert Comm(A, A) == 0
+    assert Comm(a, b) == 0
+    assert Comm(A, B) == -Comm(B, A)
+    assert Comm(A, B).doit() == A*B - B*A
+    assert Comm(A, B*C).expand(commutator=True) == Comm(A, B)*C + B*Comm(A, C)
+    assert Comm(A*B, C*D).expand(commutator=True) == \
+        A*C*Comm(B, D) + A*Comm(B, C)*D + C*Comm(A, D)*B + Comm(A, C)*D*B
+    assert Comm(A, B**2).expand(commutator=True) == Comm(A, B)*B + B*Comm(A, B)
+    assert Comm(A**2, C**2).expand(commutator=True) == \
+        Comm(A*B, C*D).expand(commutator=True).replace(B, A).replace(D, C) == \
+        A*C*Comm(A, C) + A*Comm(A, C)*C + C*Comm(A, C)*A + Comm(A, C)*C*A
+    assert Comm(A, C**-2).expand(commutator=True) == \
+        Comm(A, (1/C)*(1/D)).expand(commutator=True).replace(D, C)
+    assert Comm(A + B, C + D).expand(commutator=True) == \
+        Comm(A, C) + Comm(A, D) + Comm(B, C) + Comm(B, D)
+    assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
+    assert Comm(A**n, B).expand(commutator=True) == Comm(A**n, B)
+
+    e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
+    assert e.doit().expand() == 0
+
+
+def test_commutator_dagger():
+    comm = Comm(A*B, C)
+    assert Dagger(comm).expand(commutator=True) == \
+        - Comm(Dagger(B), Dagger(C))*Dagger(A) - \
+        Dagger(B)*Comm(Dagger(A), Dagger(C))
+
+
+class Foo(Operator):
+
+    def _eval_commutator_Bar(self, bar):
+        return Integer(0)
+
+
+class Bar(Operator):
+    pass
+
+
+class Tam(Operator):
+
+    def _eval_commutator_Foo(self, foo):
+        return Integer(1)
+
+
+def test_eval_commutator():
+    F = Foo('F')
+    B = Bar('B')
+    T = Tam('T')
+    assert Comm(F, B).doit() == 0
+    assert Comm(B, F).doit() == 0
+    assert Comm(F, T).doit() == -1
+    assert Comm(T, F).doit() == 1
+    assert Comm(B, T).doit() == B*T - T*B
+    assert Comm(F**2, B).expand(commutator=True).doit() == 0
+    assert Comm(F**2, T).expand(commutator=True).doit() == -2*F
+    assert Comm(F, T**2).expand(commutator=True).doit() == -2*T
+    assert Comm(T**2, F).expand(commutator=True).doit() == 2*T
+    assert Comm(T**2, F**3).expand(commutator=True).doit() == 2*F*T*F + 2*F**2*T + 2*T*F**2

rl/Lib/site-packages/sympy/physics/quantum/tests/test_constants.py

@@ -0,0 +1,13 @@
+from sympy.core.numbers import Float
+
+from sympy.physics.quantum.constants import hbar
+
+
+def test_hbar():
+    assert hbar.is_commutative is True
+    assert hbar.is_real is True
+    assert hbar.is_positive is True
+    assert hbar.is_negative is False
+    assert hbar.is_irrational is True
+
+    assert hbar.evalf() == Float(1.05457162e-34)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_dagger.py

@@ -0,0 +1,102 @@
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer)
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import conjugate
+from sympy.matrices.dense import Matrix
+
+from sympy.physics.quantum.dagger import adjoint, Dagger
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+from sympy.physics.quantum.operator import Operator, IdentityOperator
+
+
+def test_scalars():
+    x = symbols('x', complex=True)
+    assert Dagger(x) == conjugate(x)
+    assert Dagger(I*x) == -I*conjugate(x)
+
+    i = symbols('i', real=True)
+    assert Dagger(i) == i
+
+    p = symbols('p')
+    assert isinstance(Dagger(p), adjoint)
+
+    i = Integer(3)
+    assert Dagger(i) == i
+
+    A = symbols('A', commutative=False)
+    assert Dagger(A).is_commutative is False
+
+
+def test_matrix():
+    x = symbols('x')
+    m = Matrix([[I, x*I], [2, 4]])
+    assert Dagger(m) == m.H
+
+
+def test_dagger_mul():
+    O = Operator('O')
+    I = IdentityOperator()
+    assert Dagger(O)*O == Dagger(O)*O
+    assert Dagger(O)*O*I == Mul(Dagger(O), O)*I
+    assert Dagger(O)*Dagger(O) == Dagger(O)**2
+    assert Dagger(O)*Dagger(I) == Dagger(O)
+
+
+class Foo(Expr):
+
+    def _eval_adjoint(self):
+        return I
+
+
+def test_eval_adjoint():
+    f = Foo()
+    d = Dagger(f)
+    assert d == I
+
+np = import_module('numpy')
+
+
+def test_numpy_dagger():
+    if not np:
+        skip("numpy not installed.")
+
+    a = np.array([[1.0, 2.0j], [-1.0j, 2.0]])
+    adag = a.copy().transpose().conjugate()
+    assert (Dagger(a) == adag).all()
+
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def test_scipy_sparse_dagger():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+    else:
+        sparse = scipy.sparse
+
+    a = sparse.csr_matrix([[1.0 + 0.0j, 2.0j], [-1.0j, 2.0 + 0.0j]])
+    adag = a.copy().transpose().conjugate()
+    assert np.linalg.norm((Dagger(a) - adag).todense()) == 0.0
+
+
+def test_unknown():
+    """Check treatment of unknown objects.
+    Objects without adjoint or conjugate/transpose methods
+    are sympified and wrapped in dagger.
+    """
+    x = symbols("x")
+    result = Dagger(x)
+    assert result.args == (x,) and isinstance(result, adjoint)
+
+
+def test_unevaluated():
+    """Check that evaluate=False returns unevaluated Dagger.
+    """
+    x = symbols("x", real=True)
+    assert Dagger(x) == x
+    result = Dagger(x, evaluate=False)
+    assert result.args == (x,) and isinstance(result, adjoint)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_density.py

@@ -0,0 +1,289 @@
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import log
+from sympy.external import import_module
+from sympy.physics.quantum.density import Density, entropy, fidelity
+from sympy.physics.quantum.state import Ket, TimeDepKet
+from sympy.physics.quantum.qubit import Qubit
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.cartesian import XKet, PxKet, PxOp, XOp
+from sympy.physics.quantum.spin import JzKet
+from sympy.physics.quantum.operator import OuterProduct
+from sympy.physics.quantum.trace import Tr
+from sympy.functions import sqrt
+from sympy.testing.pytest import raises
+from sympy.physics.quantum.matrixutils import scipy_sparse_matrix
+from sympy.physics.quantum.tensorproduct import TensorProduct
+
+
+def test_eval_args():
+    # check instance created
+    assert isinstance(Density([Ket(0), 0.5], [Ket(1), 0.5]), Density)
+    assert isinstance(Density([Qubit('00'), 1/sqrt(2)],
+                              [Qubit('11'), 1/sqrt(2)]), Density)
+
+    #test if Qubit object type preserved
+    d = Density([Qubit('00'), 1/sqrt(2)], [Qubit('11'), 1/sqrt(2)])
+    for (state, prob) in d.args:
+        assert isinstance(state, Qubit)
+
+    # check for value error, when prob is not provided
+    raises(ValueError, lambda: Density([Ket(0)], [Ket(1)]))
+
+
+def test_doit():
+
+    x, y = symbols('x y')
+    A, B, C, D, E, F = symbols('A B C D E F', commutative=False)
+    d = Density([XKet(), 0.5], [PxKet(), 0.5])
+    assert (0.5*(PxKet()*Dagger(PxKet())) +
+            0.5*(XKet()*Dagger(XKet()))) == d.doit()
+
+    # check for kets with expr in them
+    d_with_sym = Density([XKet(x*y), 0.5], [PxKet(x*y), 0.5])
+    assert (0.5*(PxKet(x*y)*Dagger(PxKet(x*y))) +
+            0.5*(XKet(x*y)*Dagger(XKet(x*y)))) == d_with_sym.doit()
+
+    d = Density([(A + B)*C, 1.0])
+    assert d.doit() == (1.0*A*C*Dagger(C)*Dagger(A) +
+                        1.0*A*C*Dagger(C)*Dagger(B) +
+                        1.0*B*C*Dagger(C)*Dagger(A) +
+                        1.0*B*C*Dagger(C)*Dagger(B))
+
+    #  With TensorProducts as args
+    # Density with simple tensor products as args
+    t = TensorProduct(A, B, C)
+    d = Density([t, 1.0])
+    assert d.doit() == \
+        1.0 * TensorProduct(A*Dagger(A), B*Dagger(B), C*Dagger(C))
+
+    # Density with multiple Tensorproducts as states
+    t2 = TensorProduct(A, B)
+    t3 = TensorProduct(C, D)
+
+    d = Density([t2, 0.5], [t3, 0.5])
+    assert d.doit() == (0.5 * TensorProduct(A*Dagger(A), B*Dagger(B)) +
+                        0.5 * TensorProduct(C*Dagger(C), D*Dagger(D)))
+
+    #Density with mixed states
+    d = Density([t2 + t3, 1.0])
+    assert d.doit() == (1.0 * TensorProduct(A*Dagger(A), B*Dagger(B)) +
+                        1.0 * TensorProduct(A*Dagger(C), B*Dagger(D)) +
+                        1.0 * TensorProduct(C*Dagger(A), D*Dagger(B)) +
+                        1.0 * TensorProduct(C*Dagger(C), D*Dagger(D)))
+
+    #Density operators with spin states
+    tp1 = TensorProduct(JzKet(1, 1), JzKet(1, -1))
+    d = Density([tp1, 1])
+
+    # full trace
+    t = Tr(d)
+    assert t.doit() == 1
+
+    #Partial trace on density operators with spin states
+    t = Tr(d, [0])
+    assert t.doit() == JzKet(1, -1) * Dagger(JzKet(1, -1))
+    t = Tr(d, [1])
+    assert t.doit() == JzKet(1, 1) * Dagger(JzKet(1, 1))
+
+    # with another spin state
+    tp2 = TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))
+    d = Density([tp2, 1])
+
+    #full trace
+    t = Tr(d)
+    assert t.doit() == 1
+
+    #Partial trace on density operators with spin states
+    t = Tr(d, [0])
+    assert t.doit() == JzKet(S.Half, Rational(-1, 2)) * Dagger(JzKet(S.Half, Rational(-1, 2)))
+    t = Tr(d, [1])
+    assert t.doit() == JzKet(S.Half, S.Half) * Dagger(JzKet(S.Half, S.Half))
+
+
+def test_apply_op():
+    d = Density([Ket(0), 0.5], [Ket(1), 0.5])
+    assert d.apply_op(XOp()) == Density([XOp()*Ket(0), 0.5],
+                                        [XOp()*Ket(1), 0.5])
+
+
+def test_represent():
+    x, y = symbols('x y')
+    d = Density([XKet(), 0.5], [PxKet(), 0.5])
+    assert (represent(0.5*(PxKet()*Dagger(PxKet()))) +
+            represent(0.5*(XKet()*Dagger(XKet())))) == represent(d)
+
+    # check for kets with expr in them
+    d_with_sym = Density([XKet(x*y), 0.5], [PxKet(x*y), 0.5])
+    assert (represent(0.5*(PxKet(x*y)*Dagger(PxKet(x*y)))) +
+            represent(0.5*(XKet(x*y)*Dagger(XKet(x*y))))) == \
+        represent(d_with_sym)
+
+    # check when given explicit basis
+    assert (represent(0.5*(XKet()*Dagger(XKet())), basis=PxOp()) +
+            represent(0.5*(PxKet()*Dagger(PxKet())), basis=PxOp())) == \
+        represent(d, basis=PxOp())
+
+
+def test_states():
+    d = Density([Ket(0), 0.5], [Ket(1), 0.5])
+    states = d.states()
+    assert states[0] == Ket(0) and states[1] == Ket(1)
+
+
+def test_probs():
+    d = Density([Ket(0), .75], [Ket(1), 0.25])
+    probs = d.probs()
+    assert probs[0] == 0.75 and probs[1] == 0.25
+
+    #probs can be symbols
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    probs = d.probs()
+    assert probs[0] == x and probs[1] == y
+
+
+def test_get_state():
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    states = (d.get_state(0), d.get_state(1))
+    assert states[0] == Ket(0) and states[1] == Ket(1)
+
+
+def test_get_prob():
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    probs = (d.get_prob(0), d.get_prob(1))
+    assert probs[0] == x and probs[1] == y
+
+
+def test_entropy():
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    d = Density((up, S.Half), (down, S.Half))
+
+    # test for density object
+    ent = entropy(d)
+    assert entropy(d) == log(2)/2
+    assert d.entropy() == log(2)/2
+
+    np = import_module('numpy', min_module_version='1.4.0')
+    if np:
+        #do this test only if 'numpy' is available on test machine
+        np_mat = represent(d, format='numpy')
+        ent = entropy(np_mat)
+        assert isinstance(np_mat, np.ndarray)
+        assert ent.real == 0.69314718055994529
+        assert ent.imag == 0
+
+    scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+    if scipy and np:
+        #do this test only if numpy and scipy are available
+        mat = represent(d, format="scipy.sparse")
+        assert isinstance(mat, scipy_sparse_matrix)
+        assert ent.real == 0.69314718055994529
+        assert ent.imag == 0
+
+
+def test_eval_trace():
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    d = Density((up, 0.5), (down, 0.5))
+
+    t = Tr(d)
+    assert t.doit() == 1.0
+
+    #test dummy time dependent states
+    class TestTimeDepKet(TimeDepKet):
+        def _eval_trace(self, bra, **options):
+            return 1
+
+    x, t = symbols('x t')
+    k1 = TestTimeDepKet(0, 0.5)
+    k2 = TestTimeDepKet(0, 1)
+    d = Density([k1, 0.5], [k2, 0.5])
+    assert d.doit() == (0.5 * OuterProduct(k1, k1.dual) +
+                        0.5 * OuterProduct(k2, k2.dual))
+
+    t = Tr(d)
+    assert t.doit() == 1.0
+
+
+def test_fidelity():
+    #test with kets
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    updown = (S.One/sqrt(2))*up + (S.One/sqrt(2))*down
+
+    #check with matrices
+    up_dm = represent(up * Dagger(up))
+    down_dm = represent(down * Dagger(down))
+    updown_dm = represent(updown * Dagger(updown))
+
+    assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
+    assert fidelity(up_dm, down_dm) < 1e-3
+    assert abs(fidelity(up_dm, updown_dm) - (S.One/sqrt(2))) < 1e-3
+    assert abs(fidelity(updown_dm, down_dm) - (S.One/sqrt(2))) < 1e-3
+
+    #check with density
+    up_dm = Density([up, 1.0])
+    down_dm = Density([down, 1.0])
+    updown_dm = Density([updown, 1.0])
+
+    assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
+    assert abs(fidelity(up_dm, down_dm)) < 1e-3
+    assert abs(fidelity(up_dm, updown_dm) - (S.One/sqrt(2))) < 1e-3
+    assert abs(fidelity(updown_dm, down_dm) - (S.One/sqrt(2))) < 1e-3
+
+    #check mixed states with density
+    updown2 = sqrt(3)/2*up + S.Half*down
+    d1 = Density([updown, 0.25], [updown2, 0.75])
+    d2 = Density([updown, 0.75], [updown2, 0.25])
+    assert abs(fidelity(d1, d2) - 0.991) < 1e-3
+    assert abs(fidelity(d2, d1) - fidelity(d1, d2)) < 1e-3
+
+    #using qubits/density(pure states)
+    state1 = Qubit('0')
+    state2 = Qubit('1')
+    state3 = S.One/sqrt(2)*state1 + S.One/sqrt(2)*state2
+    state4 = sqrt(Rational(2, 3))*state1 + S.One/sqrt(3)*state2
+
+    state1_dm = Density([state1, 1])
+    state2_dm = Density([state2, 1])
+    state3_dm = Density([state3, 1])
+
+    assert fidelity(state1_dm, state1_dm) == 1
+    assert fidelity(state1_dm, state2_dm) == 0
+    assert abs(fidelity(state1_dm, state3_dm) - 1/sqrt(2)) < 1e-3
+    assert abs(fidelity(state3_dm, state2_dm) - 1/sqrt(2)) < 1e-3
+
+    #using qubits/density(mixed states)
+    d1 = Density([state3, 0.70], [state4, 0.30])
+    d2 = Density([state3, 0.20], [state4, 0.80])
+    assert abs(fidelity(d1, d1) - 1) < 1e-3
+    assert abs(fidelity(d1, d2) - 0.996) < 1e-3
+    assert abs(fidelity(d1, d2) - fidelity(d2, d1)) < 1e-3
+
+    #TODO: test for invalid arguments
+    # non-square matrix
+    mat1 = [[0, 0],
+            [0, 0],
+            [0, 0]]
+
+    mat2 = [[0, 0],
+            [0, 0]]
+    raises(ValueError, lambda: fidelity(mat1, mat2))
+
+    # unequal dimensions
+    mat1 = [[0, 0],
+            [0, 0]]
+    mat2 = [[0, 0, 0],
+            [0, 0, 0],
+            [0, 0, 0]]
+    raises(ValueError, lambda: fidelity(mat1, mat2))
+
+    # unsupported data-type
+    x, y = 1, 2  # random values that is not a matrix
+    raises(ValueError, lambda: fidelity(x, y))

rl/Lib/site-packages/sympy/physics/quantum/tests/test_fermion.py

@@ -0,0 +1,62 @@
+from pytest import raises
+
+import sympy
+from sympy.physics.quantum import Dagger, AntiCommutator, qapply
+from sympy.physics.quantum.fermion import FermionOp
+from sympy.physics.quantum.fermion import FermionFockKet, FermionFockBra
+from sympy import Symbol
+
+
+def test_fermionoperator():
+    c = FermionOp('c')
+    d = FermionOp('d')
+
+    assert isinstance(c, FermionOp)
+    assert isinstance(Dagger(c), FermionOp)
+
+    assert c.is_annihilation
+    assert not Dagger(c).is_annihilation
+
+    assert FermionOp("c") == FermionOp("c", True)
+    assert FermionOp("c") != FermionOp("d")
+    assert FermionOp("c", True) != FermionOp("c", False)
+
+    assert AntiCommutator(c, Dagger(c)).doit() == 1
+
+    assert AntiCommutator(c, Dagger(d)).doit() == c * Dagger(d) + Dagger(d) * c
+
+
+def test_fermion_states():
+    c = FermionOp("c")
+
+    # Fock states
+    assert (FermionFockBra(0) * FermionFockKet(1)).doit() == 0
+    assert (FermionFockBra(1) * FermionFockKet(1)).doit() == 1
+
+    assert qapply(c * FermionFockKet(1)) == FermionFockKet(0)
+    assert qapply(c * FermionFockKet(0)) == 0
+
+    assert qapply(Dagger(c) * FermionFockKet(0)) == FermionFockKet(1)
+    assert qapply(Dagger(c) * FermionFockKet(1)) == 0
+
+
+def test_power():
+    c = FermionOp("c")
+    assert c**0 == 1
+    assert c**1 == c
+    assert c**2 == 0
+    assert c**3 == 0
+    assert Dagger(c)**1 == Dagger(c)
+    assert Dagger(c)**2 == 0
+
+    assert (c**Symbol('a')).func == sympy.core.power.Pow
+    assert (c**Symbol('a')).args == (c, Symbol('a'))
+
+    with raises(ValueError):
+        c**-1
+
+    with raises(ValueError):
+        c**3.2
+
+    with raises(TypeError):
+        c**1j

rl/Lib/site-packages/sympy/physics/quantum/tests/test_gate.py

@@ -0,0 +1,360 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer, Rational, pi)
+from sympy.core.symbol import (Wild, symbols)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices import Matrix, ImmutableMatrix
+
+from sympy.physics.quantum.gate import (XGate, YGate, ZGate, random_circuit,
+        CNOT, IdentityGate, H, X, Y, S, T, Z, SwapGate, gate_simp, gate_sort,
+        CNotGate, TGate, HadamardGate, PhaseGate, UGate, CGate)
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qubit import Qubit, IntQubit, qubit_to_matrix, \
+    matrix_to_qubit
+from sympy.physics.quantum.matrixutils import matrix_to_zero
+from sympy.physics.quantum.matrixcache import sqrt2_inv
+from sympy.physics.quantum import Dagger
+
+
+def test_gate():
+    """Test a basic gate."""
+    h = HadamardGate(1)
+    assert h.min_qubits == 2
+    assert h.nqubits == 1
+
+    i0 = Wild('i0')
+    i1 = Wild('i1')
+    h0_w1 = HadamardGate(i0)
+    h0_w2 = HadamardGate(i0)
+    h1_w1 = HadamardGate(i1)
+
+    assert h0_w1 == h0_w2
+    assert h0_w1 != h1_w1
+    assert h1_w1 != h0_w2
+
+    cnot_10_w1 = CNOT(i1, i0)
+    cnot_10_w2 = CNOT(i1, i0)
+    cnot_01_w1 = CNOT(i0, i1)
+
+    assert cnot_10_w1 == cnot_10_w2
+    assert cnot_10_w1 != cnot_01_w1
+    assert cnot_10_w2 != cnot_01_w1
+
+
+def test_UGate():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+
+    # Test basic case where gate exists in 1-qubit space
+    u1 = UGate((0,), uMat)
+    assert represent(u1, nqubits=1) == uMat
+    assert qapply(u1*Qubit('0')) == a*Qubit('0') + c*Qubit('1')
+    assert qapply(u1*Qubit('1')) == b*Qubit('0') + d*Qubit('1')
+
+    # Test case where gate exists in a larger space
+    u2 = UGate((1,), uMat)
+    u2Rep = represent(u2, nqubits=2)
+    for i in range(4):
+        assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
+            qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
+
+
+def test_cgate():
+    """Test the general CGate."""
+    # Test single control functionality
+    CNOTMatrix = Matrix(
+        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+    assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix
+
+    # Test multiple control bit functionality
+    ToffoliGate = CGate((1, 2), XGate(0))
+    assert represent(ToffoliGate, nqubits=3) == \
+        Matrix(
+            [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0],
+    [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0,
+        1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1],
+    [0, 0, 0, 0, 0, 0, 1, 0]])
+
+    ToffoliGate = CGate((3, 0), XGate(1))
+    assert qapply(ToffoliGate*Qubit('1001')) == \
+        matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4))
+    assert qapply(ToffoliGate*Qubit('0000')) == \
+        matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4))
+
+    CYGate = CGate(1, YGate(0))
+    CYGate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, -I), (0, 0, I, 0)))
+    # Test 2 qubit controlled-Y gate decompose method.
+    assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix
+
+    CZGate = CGate(0, ZGate(1))
+    CZGate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1)))
+    assert qapply(CZGate*Qubit('11')) == -Qubit('11')
+    assert matrix_to_qubit(represent(CZGate*Qubit('11'), nqubits=2)) == \
+        -Qubit('11')
+    # Test 2 qubit controlled-Z gate decompose method.
+    assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix
+
+    CPhaseGate = CGate(0, PhaseGate(1))
+    assert qapply(CPhaseGate*Qubit('11')) == \
+        I*Qubit('11')
+    assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \
+        I*Qubit('11')
+
+    # Test that the dagger, inverse, and power of CGate is evaluated properly
+    assert Dagger(CZGate) == CZGate
+    assert pow(CZGate, 1) == Dagger(CZGate)
+    assert Dagger(CZGate) == CZGate.inverse()
+    assert Dagger(CPhaseGate) != CPhaseGate
+    assert Dagger(CPhaseGate) == CPhaseGate.inverse()
+    assert Dagger(CPhaseGate) == pow(CPhaseGate, -1)
+    assert pow(CPhaseGate, -1) == CPhaseGate.inverse()
+
+
+def test_UGate_CGate_combo():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+    cMat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, a, b], [0, 0, c, d]])
+
+    # Test basic case where gate exists in 1-qubit space.
+    u1 = UGate((0,), uMat)
+    cu1 = CGate(1, u1)
+    assert represent(cu1, nqubits=2) == cMat
+    assert qapply(cu1*Qubit('10')) == a*Qubit('10') + c*Qubit('11')
+    assert qapply(cu1*Qubit('11')) == b*Qubit('10') + d*Qubit('11')
+    assert qapply(cu1*Qubit('01')) == Qubit('01')
+    assert qapply(cu1*Qubit('00')) == Qubit('00')
+
+    # Test case where gate exists in a larger space.
+    u2 = UGate((1,), uMat)
+    u2Rep = represent(u2, nqubits=2)
+    for i in range(4):
+        assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
+            qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
+
+def test_UGate_OneQubitGate_combo():
+    v, w, f, g = symbols('v w f g')
+    uMat1 = ImmutableMatrix([[v, w], [f, g]])
+    cMat1 = Matrix([[v, w + 1, 0, 0], [f + 1, g, 0, 0], [0, 0, v, w + 1], [0, 0, f + 1, g]])
+    u1 = X(0) + UGate(0, uMat1)
+    assert represent(u1, nqubits=2) == cMat1
+
+    uMat2 = ImmutableMatrix([[1/sqrt(2), 1/sqrt(2)], [I/sqrt(2), -I/sqrt(2)]])
+    cMat2_1 = Matrix([[Rational(1, 2) + I/2, Rational(1, 2) - I/2],
+                      [Rational(1, 2) - I/2, Rational(1, 2) + I/2]])
+    cMat2_2 = Matrix([[1, 0], [0, I]])
+    u2 = UGate(0, uMat2)
+    assert represent(H(0)*u2, nqubits=1) == cMat2_1
+    assert represent(u2*H(0), nqubits=1) == cMat2_2
+
+def test_represent_hadamard():
+    """Test the representation of the hadamard gate."""
+    circuit = HadamardGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    # Check that the answers are same to within an epsilon.
+    assert answer == Matrix([sqrt2_inv, sqrt2_inv, 0, 0])
+
+
+def test_represent_xgate():
+    """Test the representation of the X gate."""
+    circuit = XGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([0, 1, 0, 0]) == answer
+
+
+def test_represent_ygate():
+    """Test the representation of the Y gate."""
+    circuit = YGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert answer[0] == 0 and answer[1] == I and \
+        answer[2] == 0 and answer[3] == 0
+
+
+def test_represent_zgate():
+    """Test the representation of the Z gate."""
+    circuit = ZGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([1, 0, 0, 0]) == answer
+
+
+def test_represent_phasegate():
+    """Test the representation of the S gate."""
+    circuit = PhaseGate(0)*Qubit('01')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([0, I, 0, 0]) == answer
+
+
+def test_represent_tgate():
+    """Test the representation of the T gate."""
+    circuit = TGate(0)*Qubit('01')
+    assert Matrix([0, exp(I*pi/4), 0, 0]) == represent(circuit, nqubits=2)
+
+
+def test_compound_gates():
+    """Test a compound gate representation."""
+    circuit = YGate(0)*ZGate(0)*XGate(0)*HadamardGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([I/sqrt(2), I/sqrt(2), 0, 0]) == answer
+
+
+def test_cnot_gate():
+    """Test the CNOT gate."""
+    circuit = CNotGate(1, 0)
+    assert represent(circuit, nqubits=2) == \
+        Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+    circuit = circuit*Qubit('111')
+    assert matrix_to_qubit(represent(circuit, nqubits=3)) == \
+        qapply(circuit)
+
+    circuit = CNotGate(1, 0)
+    assert Dagger(circuit) == circuit
+    assert Dagger(Dagger(circuit)) == circuit
+    assert circuit*circuit == 1
+
+
+def test_gate_sort():
+    """Test gate_sort."""
+    for g in (X, Y, Z, H, S, T):
+        assert gate_sort(g(2)*g(1)*g(0)) == g(0)*g(1)*g(2)
+    e = gate_sort(X(1)*H(0)**2*CNOT(0, 1)*X(1)*X(0))
+    assert e == H(0)**2*CNOT(0, 1)*X(0)*X(1)**2
+    assert gate_sort(Z(0)*X(0)) == -X(0)*Z(0)
+    assert gate_sort(Z(0)*X(0)**2) == X(0)**2*Z(0)
+    assert gate_sort(Y(0)*H(0)) == -H(0)*Y(0)
+    assert gate_sort(Y(0)*X(0)) == -X(0)*Y(0)
+    assert gate_sort(Z(0)*Y(0)) == -Y(0)*Z(0)
+    assert gate_sort(T(0)*S(0)) == S(0)*T(0)
+    assert gate_sort(Z(0)*S(0)) == S(0)*Z(0)
+    assert gate_sort(Z(0)*T(0)) == T(0)*Z(0)
+    assert gate_sort(Z(0)*CNOT(0, 1)) == CNOT(0, 1)*Z(0)
+    assert gate_sort(S(0)*CNOT(0, 1)) == CNOT(0, 1)*S(0)
+    assert gate_sort(T(0)*CNOT(0, 1)) == CNOT(0, 1)*T(0)
+    assert gate_sort(X(1)*CNOT(0, 1)) == CNOT(0, 1)*X(1)
+    # This takes a long time and should only be uncommented once in a while.
+    # nqubits = 5
+    # ngates = 10
+    # trials = 10
+    # for i in range(trials):
+    #     c = random_circuit(ngates, nqubits)
+    #     assert represent(c, nqubits=nqubits) == \
+    #            represent(gate_sort(c), nqubits=nqubits)
+
+
+def test_gate_simp():
+    """Test gate_simp."""
+    e = H(0)*X(1)*H(0)**2*CNOT(0, 1)*X(1)**3*X(0)*Z(3)**2*S(4)**3
+    assert gate_simp(e) == H(0)*CNOT(0, 1)*S(4)*X(0)*Z(4)
+    assert gate_simp(X(0)*X(0)) == 1
+    assert gate_simp(Y(0)*Y(0)) == 1
+    assert gate_simp(Z(0)*Z(0)) == 1
+    assert gate_simp(H(0)*H(0)) == 1
+    assert gate_simp(T(0)*T(0)) == S(0)
+    assert gate_simp(S(0)*S(0)) == Z(0)
+    assert gate_simp(Integer(1)) == Integer(1)
+    assert gate_simp(X(0)**2 + Y(0)**2) == Integer(2)
+
+
+def test_swap_gate():
+    """Test the SWAP gate."""
+    swap_gate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 0, 1, 0), (0, 1, 0, 0), (0, 0, 0, 1)))
+    assert represent(SwapGate(1, 0).decompose(), nqubits=2) == swap_gate_matrix
+    assert qapply(SwapGate(1, 3)*Qubit('0010')) == Qubit('1000')
+    nqubits = 4
+    for i in range(nqubits):
+        for j in range(i):
+            assert represent(SwapGate(i, j), nqubits=nqubits) == \
+                represent(SwapGate(i, j).decompose(), nqubits=nqubits)
+
+
+def test_one_qubit_commutators():
+    """Test single qubit gate commutation relations."""
+    for g1 in (IdentityGate, X, Y, Z, H, T, S):
+        for g2 in (IdentityGate, X, Y, Z, H, T, S):
+            e = Commutator(g1(0), g2(0))
+            a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
+            assert a == b
+
+            e = Commutator(g1(0), g2(1))
+            assert e.doit() == 0
+
+
+def test_one_qubit_anticommutators():
+    """Test single qubit gate anticommutation relations."""
+    for g1 in (IdentityGate, X, Y, Z, H):
+        for g2 in (IdentityGate, X, Y, Z, H):
+            e = AntiCommutator(g1(0), g2(0))
+            a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
+            assert a == b
+            e = AntiCommutator(g1(0), g2(1))
+            a = matrix_to_zero(represent(e, nqubits=2, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=2, format='sympy'))
+            assert a == b
+
+
+def test_cnot_commutators():
+    """Test commutators of involving CNOT gates."""
+    assert Commutator(CNOT(0, 1), Z(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), T(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), S(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), X(1)).doit() == 0
+    assert Commutator(CNOT(0, 1), CNOT(0, 1)).doit() == 0
+    assert Commutator(CNOT(0, 1), CNOT(0, 2)).doit() == 0
+    assert Commutator(CNOT(0, 2), CNOT(0, 1)).doit() == 0
+    assert Commutator(CNOT(1, 2), CNOT(1, 0)).doit() == 0
+
+
+def test_random_circuit():
+    c = random_circuit(10, 3)
+    assert isinstance(c, Mul)
+    m = represent(c, nqubits=3)
+    assert m.shape == (8, 8)
+    assert isinstance(m, Matrix)
+
+
+def test_hermitian_XGate():
+    x = XGate(1, 2)
+    x_dagger = Dagger(x)
+
+    assert (x == x_dagger)
+
+
+def test_hermitian_YGate():
+    y = YGate(1, 2)
+    y_dagger = Dagger(y)
+
+    assert (y == y_dagger)
+
+
+def test_hermitian_ZGate():
+    z = ZGate(1, 2)
+    z_dagger = Dagger(z)
+
+    assert (z == z_dagger)
+
+
+def test_unitary_XGate():
+    x = XGate(1, 2)
+    x_dagger = Dagger(x)
+
+    assert (x*x_dagger == 1)
+
+
+def test_unitary_YGate():
+    y = YGate(1, 2)
+    y_dagger = Dagger(y)
+
+    assert (y*y_dagger == 1)
+
+
+def test_unitary_ZGate():
+    z = ZGate(1, 2)
+    z_dagger = Dagger(z)
+
+    assert (z*z_dagger == 1)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_grover.py

@@ -0,0 +1,92 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import Matrix
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qubit import IntQubit
+from sympy.physics.quantum.grover import (apply_grover, superposition_basis,
+        OracleGate, grover_iteration, WGate)
+
+
+def return_one_on_two(qubits):
+    return qubits == IntQubit(2, qubits.nqubits)
+
+
+def return_one_on_one(qubits):
+    return qubits == IntQubit(1, nqubits=qubits.nqubits)
+
+
+def test_superposition_basis():
+    nbits = 2
+    first_half_state = IntQubit(0, nqubits=nbits)/2 + IntQubit(1, nqubits=nbits)/2
+    second_half_state = IntQubit(2, nbits)/2 + IntQubit(3, nbits)/2
+    assert first_half_state + second_half_state == superposition_basis(nbits)
+
+    nbits = 3
+    firstq = (1/sqrt(8))*IntQubit(0, nqubits=nbits) + (1/sqrt(8))*IntQubit(1, nqubits=nbits)
+    secondq = (1/sqrt(8))*IntQubit(2, nbits) + (1/sqrt(8))*IntQubit(3, nbits)
+    thirdq = (1/sqrt(8))*IntQubit(4, nbits) + (1/sqrt(8))*IntQubit(5, nbits)
+    fourthq = (1/sqrt(8))*IntQubit(6, nbits) + (1/sqrt(8))*IntQubit(7, nbits)
+    assert firstq + secondq + thirdq + fourthq == superposition_basis(nbits)
+
+
+def test_OracleGate():
+    v = OracleGate(1, lambda qubits: qubits == IntQubit(0))
+    assert qapply(v*IntQubit(0)) == -IntQubit(0)
+    assert qapply(v*IntQubit(1)) == IntQubit(1)
+
+    nbits = 2
+    v = OracleGate(2, return_one_on_two)
+    assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nqubits=nbits)
+    assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nqubits=nbits)
+    assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits)
+    assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits)
+
+    assert represent(OracleGate(1, lambda qubits: qubits == IntQubit(0)), nqubits=1) == \
+           Matrix([[-1, 0], [0, 1]])
+    assert represent(v, nqubits=2) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]])
+
+
+def test_WGate():
+    nqubits = 2
+    basis_states = superposition_basis(nqubits)
+    assert qapply(WGate(nqubits)*basis_states) == basis_states
+
+    expected = ((2/sqrt(pow(2, nqubits)))*basis_states) - IntQubit(1, nqubits=nqubits)
+    assert qapply(WGate(nqubits)*IntQubit(1, nqubits=nqubits)) == expected
+
+
+def test_grover_iteration_1():
+    numqubits = 2
+    basis_states = superposition_basis(numqubits)
+    v = OracleGate(numqubits, return_one_on_one)
+    expected = IntQubit(1, nqubits=numqubits)
+    assert qapply(grover_iteration(basis_states, v)) == expected
+
+
+def test_grover_iteration_2():
+    numqubits = 4
+    basis_states = superposition_basis(numqubits)
+    v = OracleGate(numqubits, return_one_on_two)
+    # After (pi/4)sqrt(pow(2, n)), IntQubit(2) should have highest prob
+    # In this case, after around pi times (3 or 4)
+    iterated = grover_iteration(basis_states, v)
+    iterated = qapply(iterated)
+    iterated = grover_iteration(iterated, v)
+    iterated = qapply(iterated)
+    iterated = grover_iteration(iterated, v)
+    iterated = qapply(iterated)
+    # In this case, probability was highest after 3 iterations
+    # Probability of Qubit('0010') was 251/256 (3) vs 781/1024 (4)
+    # Ask about measurement
+    expected = (-13*basis_states)/64 + 264*IntQubit(2, numqubits)/256
+    assert qapply(expected) == iterated
+
+
+def test_grover():
+    nqubits = 2
+    assert apply_grover(return_one_on_one, nqubits) == IntQubit(1, nqubits=nqubits)
+
+    nqubits = 4
+    basis_states = superposition_basis(nqubits)
+    expected = (-13*basis_states)/64 + 264*IntQubit(2, nqubits)/256
+    assert apply_grover(return_one_on_two, 4) == qapply(expected)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_hilbert.py

@@ -0,0 +1,110 @@
+from sympy.physics.quantum.hilbert import (
+    HilbertSpace, ComplexSpace, L2, FockSpace, TensorProductHilbertSpace,
+    DirectSumHilbertSpace, TensorPowerHilbertSpace
+)
+
+from sympy.core.numbers import oo
+from sympy.core.symbol import Symbol
+from sympy.printing.repr import srepr
+from sympy.printing.str import sstr
+from sympy.sets.sets import Interval
+
+
+def test_hilbert_space():
+    hs = HilbertSpace()
+    assert isinstance(hs, HilbertSpace)
+    assert sstr(hs) == 'H'
+    assert srepr(hs) == 'HilbertSpace()'
+
+
+def test_complex_space():
+    c1 = ComplexSpace(2)
+    assert isinstance(c1, ComplexSpace)
+    assert c1.dimension == 2
+    assert sstr(c1) == 'C(2)'
+    assert srepr(c1) == 'ComplexSpace(Integer(2))'
+
+    n = Symbol('n')
+    c2 = ComplexSpace(n)
+    assert isinstance(c2, ComplexSpace)
+    assert c2.dimension == n
+    assert sstr(c2) == 'C(n)'
+    assert srepr(c2) == "ComplexSpace(Symbol('n'))"
+    assert c2.subs(n, 2) == ComplexSpace(2)
+
+
+def test_L2():
+    b1 = L2(Interval(-oo, 1))
+    assert isinstance(b1, L2)
+    assert b1.dimension is oo
+    assert b1.interval == Interval(-oo, 1)
+
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    b2 = L2(Interval(x, y))
+    assert b2.dimension is oo
+    assert b2.interval == Interval(x, y)
+    assert b2.subs(x, -1) == L2(Interval(-1, y))
+
+
+def test_fock_space():
+    f1 = FockSpace()
+    f2 = FockSpace()
+    assert isinstance(f1, FockSpace)
+    assert f1.dimension is oo
+    assert f1 == f2
+
+
+def test_tensor_product():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1*hs2
+    assert isinstance(h, TensorProductHilbertSpace)
+    assert h.dimension == 2*n
+    assert h.spaces == (hs1, hs2)
+
+    h = hs2*hs2
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs2
+    assert h.exp == 2
+    assert h.dimension == n**2
+
+    f = FockSpace()
+    h = hs1*hs2*f
+    assert h.dimension is oo
+
+
+def test_tensor_power():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1**2
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs1
+    assert h.exp == 2
+    assert h.dimension == 4
+
+    h = hs2**3
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs2
+    assert h.exp == 3
+    assert h.dimension == n**3
+
+
+def test_direct_sum():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1 + hs2
+    assert isinstance(h, DirectSumHilbertSpace)
+    assert h.dimension == 2 + n
+    assert h.spaces == (hs1, hs2)
+
+    f = FockSpace()
+    h = hs1 + f + hs2
+    assert h.dimension is oo
+    assert h.spaces == (hs1, f, hs2)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_identitysearch.py

@@ -0,0 +1,492 @@
+from sympy.external import import_module
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.gate import (X, Y, Z, H, CNOT,
+        IdentityGate, CGate, PhaseGate, TGate)
+from sympy.physics.quantum.identitysearch import (generate_gate_rules,
+        generate_equivalent_ids, GateIdentity, bfs_identity_search,
+        is_scalar_sparse_matrix,
+        is_scalar_nonsparse_matrix, is_degenerate, is_reducible)
+from sympy.testing.pytest import skip
+
+
+def create_gate_sequence(qubit=0):
+    gates = (X(qubit), Y(qubit), Z(qubit), H(qubit))
+    return gates
+
+
+def test_generate_gate_rules_1():
+    # Test with tuples
+    (x, y, z, h) = create_gate_sequence()
+    ph = PhaseGate(0)
+    cgate_t = CGate(0, TGate(1))
+
+    assert generate_gate_rules((x,)) == {((x,), ())}
+
+    gate_rules = {((x, x), ()),
+                      ((x,), (x,))}
+    assert generate_gate_rules((x, x)) == gate_rules
+
+    gate_rules = {((x, y, x), ()),
+                      ((y, x, x), ()),
+                      ((x, x, y), ()),
+                      ((y, x), (x,)),
+                      ((x, y), (x,)),
+                      ((y,), (x, x))}
+    assert generate_gate_rules((x, y, x)) == gate_rules
+
+    gate_rules = {((x, y, z), ()), ((y, z, x), ()), ((z, x, y), ()),
+                      ((), (x, z, y)), ((), (y, x, z)), ((), (z, y, x)),
+                      ((x,), (z, y)), ((y, z), (x,)), ((y,), (x, z)),
+                      ((z, x), (y,)), ((z,), (y, x)), ((x, y), (z,))}
+    actual = generate_gate_rules((x, y, z))
+    assert actual == gate_rules
+
+    gate_rules = {
+        ((), (h, z, y, x)), ((), (x, h, z, y)), ((), (y, x, h, z)),
+         ((), (z, y, x, h)), ((h,), (z, y, x)), ((x,), (h, z, y)),
+         ((y,), (x, h, z)), ((z,), (y, x, h)), ((h, x), (z, y)),
+         ((x, y), (h, z)), ((y, z), (x, h)), ((z, h), (y, x)),
+         ((h, x, y), (z,)), ((x, y, z), (h,)), ((y, z, h), (x,)),
+         ((z, h, x), (y,)), ((h, x, y, z), ()), ((x, y, z, h), ()),
+         ((y, z, h, x), ()), ((z, h, x, y), ())}
+    actual = generate_gate_rules((x, y, z, h))
+    assert actual == gate_rules
+
+    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
+                      ((), (ph**(-1), x, cgate_t**(-1))),
+                      ((), (x, cgate_t**(-1), ph**(-1))),
+                      ((cgate_t,), (ph**(-1), x)),
+                      ((ph,), (x, cgate_t**(-1))),
+                      ((x,), (cgate_t**(-1), ph**(-1))),
+                      ((cgate_t, x), (ph**(-1),)),
+                      ((ph, cgate_t), (x,)),
+                      ((x, ph), (cgate_t**(-1),)),
+                      ((cgate_t, x, ph), ()),
+                      ((ph, cgate_t, x), ()),
+                      ((x, ph, cgate_t), ())}
+    actual = generate_gate_rules((x, ph, cgate_t))
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
+                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
+                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
+                      (cgate_t, ph**(-1)*x),
+                      (ph, x*cgate_t**(-1)),
+                      (x, cgate_t**(-1)*ph**(-1)),
+                      (cgate_t*x, ph**(-1)),
+                      (ph*cgate_t, x),
+                      (x*ph, cgate_t**(-1)),
+                      (cgate_t*x*ph, Integer(1)),
+                      (ph*cgate_t*x, Integer(1)),
+                      (x*ph*cgate_t, Integer(1))}
+    actual = generate_gate_rules((x, ph, cgate_t), return_as_muls=True)
+    assert actual == gate_rules
+
+
+def test_generate_gate_rules_2():
+    # Test with Muls
+    (x, y, z, h) = create_gate_sequence()
+    ph = PhaseGate(0)
+    cgate_t = CGate(0, TGate(1))
+
+    # Note: 1 (type int) is not the same as 1 (type One)
+    expected = {(x, Integer(1))}
+    assert generate_gate_rules((x,), return_as_muls=True) == expected
+
+    expected = {(Integer(1), Integer(1))}
+    assert generate_gate_rules(x*x, return_as_muls=True) == expected
+
+    expected = {((), ())}
+    assert generate_gate_rules(x*x, return_as_muls=False) == expected
+
+    gate_rules = {(x*y*x, Integer(1)),
+                      (y, Integer(1)),
+                      (y*x, x),
+                      (x*y, x)}
+    assert generate_gate_rules(x*y*x, return_as_muls=True) == gate_rules
+
+    gate_rules = {(x*y*z, Integer(1)),
+                      (y*z*x, Integer(1)),
+                      (z*x*y, Integer(1)),
+                      (Integer(1), x*z*y),
+                      (Integer(1), y*x*z),
+                      (Integer(1), z*y*x),
+                      (x, z*y),
+                      (y*z, x),
+                      (y, x*z),
+                      (z*x, y),
+                      (z, y*x),
+                      (x*y, z)}
+    actual = generate_gate_rules(x*y*z, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), h*z*y*x),
+                      (Integer(1), x*h*z*y),
+                      (Integer(1), y*x*h*z),
+                      (Integer(1), z*y*x*h),
+                      (h, z*y*x), (x, h*z*y),
+                      (y, x*h*z), (z, y*x*h),
+                      (h*x, z*y), (z*h, y*x),
+                      (x*y, h*z), (y*z, x*h),
+                      (h*x*y, z), (x*y*z, h),
+                      (y*z*h, x), (z*h*x, y),
+                      (h*x*y*z, Integer(1)),
+                      (x*y*z*h, Integer(1)),
+                      (y*z*h*x, Integer(1)),
+                      (z*h*x*y, Integer(1))}
+    actual = generate_gate_rules(x*y*z*h, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
+                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
+                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
+                      (cgate_t, ph**(-1)*x),
+                      (ph, x*cgate_t**(-1)),
+                      (x, cgate_t**(-1)*ph**(-1)),
+                      (cgate_t*x, ph**(-1)),
+                      (ph*cgate_t, x),
+                      (x*ph, cgate_t**(-1)),
+                      (cgate_t*x*ph, Integer(1)),
+                      (ph*cgate_t*x, Integer(1)),
+                      (x*ph*cgate_t, Integer(1))}
+    actual = generate_gate_rules(x*ph*cgate_t, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
+                      ((), (ph**(-1), x, cgate_t**(-1))),
+                      ((), (x, cgate_t**(-1), ph**(-1))),
+                      ((cgate_t,), (ph**(-1), x)),
+                      ((ph,), (x, cgate_t**(-1))),
+                      ((x,), (cgate_t**(-1), ph**(-1))),
+                      ((cgate_t, x), (ph**(-1),)),
+                      ((ph, cgate_t), (x,)),
+                      ((x, ph), (cgate_t**(-1),)),
+                      ((cgate_t, x, ph), ()),
+                      ((ph, cgate_t, x), ()),
+                      ((x, ph, cgate_t), ())}
+    actual = generate_gate_rules(x*ph*cgate_t)
+    assert actual == gate_rules
+
+
+def test_generate_equivalent_ids_1():
+    # Test with tuples
+    (x, y, z, h) = create_gate_sequence()
+
+    assert generate_equivalent_ids((x,)) == {(x,)}
+    assert generate_equivalent_ids((x, x)) == {(x, x)}
+    assert generate_equivalent_ids((x, y)) == {(x, y), (y, x)}
+
+    gate_seq = (x, y, z)
+    gate_ids = {(x, y, z), (y, z, x), (z, x, y), (z, y, x),
+                    (y, x, z), (x, z, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    gate_ids = {Mul(x, y, z), Mul(y, z, x), Mul(z, x, y),
+                    Mul(z, y, x), Mul(y, x, z), Mul(x, z, y)}
+    assert generate_equivalent_ids(gate_seq, return_as_muls=True) == gate_ids
+
+    gate_seq = (x, y, z, h)
+    gate_ids = {(x, y, z, h), (y, z, h, x),
+                    (h, x, y, z), (h, z, y, x),
+                    (z, y, x, h), (y, x, h, z),
+                    (z, h, x, y), (x, h, z, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    gate_seq = (x, y, x, y)
+    gate_ids = {(x, y, x, y), (y, x, y, x)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    cgate_y = CGate((1,), y)
+    gate_seq = (y, cgate_y, y, cgate_y)
+    gate_ids = {(y, cgate_y, y, cgate_y), (cgate_y, y, cgate_y, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+    gate_seq = (cnot, h, cgate_z, h)
+    gate_ids = {(cnot, h, cgate_z, h), (h, cgate_z, h, cnot),
+                    (h, cnot, h, cgate_z), (cgate_z, h, cnot, h)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+
+def test_generate_equivalent_ids_2():
+    # Test with Muls
+    (x, y, z, h) = create_gate_sequence()
+
+    assert generate_equivalent_ids((x,), return_as_muls=True) == {x}
+
+    gate_ids = {Integer(1)}
+    assert generate_equivalent_ids(x*x, return_as_muls=True) == gate_ids
+
+    gate_ids = {x*y, y*x}
+    assert generate_equivalent_ids(x*y, return_as_muls=True) == gate_ids
+
+    gate_ids = {(x, y), (y, x)}
+    assert generate_equivalent_ids(x*y) == gate_ids
+
+    circuit = Mul(*(x, y, z))
+    gate_ids = {x*y*z, y*z*x, z*x*y, z*y*x,
+                    y*x*z, x*z*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    circuit = Mul(*(x, y, z, h))
+    gate_ids = {x*y*z*h, y*z*h*x,
+                    h*x*y*z, h*z*y*x,
+                    z*y*x*h, y*x*h*z,
+                    z*h*x*y, x*h*z*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    circuit = Mul(*(x, y, x, y))
+    gate_ids = {x*y*x*y, y*x*y*x}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    cgate_y = CGate((1,), y)
+    circuit = Mul(*(y, cgate_y, y, cgate_y))
+    gate_ids = {y*cgate_y*y*cgate_y, cgate_y*y*cgate_y*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+    circuit = Mul(*(cnot, h, cgate_z, h))
+    gate_ids = {cnot*h*cgate_z*h, h*cgate_z*h*cnot,
+                    h*cnot*h*cgate_z, cgate_z*h*cnot*h}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+
+def test_is_scalar_nonsparse_matrix():
+    numqubits = 2
+    id_only = False
+
+    id_gate = (IdentityGate(1),)
+    actual = is_scalar_nonsparse_matrix(id_gate, numqubits, id_only)
+    assert actual is True
+
+    x0 = X(0)
+    xx_circuit = (x0, x0)
+    actual = is_scalar_nonsparse_matrix(xx_circuit, numqubits, id_only)
+    assert actual is True
+
+    x1 = X(1)
+    y1 = Y(1)
+    xy_circuit = (x1, y1)
+    actual = is_scalar_nonsparse_matrix(xy_circuit, numqubits, id_only)
+    assert actual is False
+
+    z1 = Z(1)
+    xyz_circuit = (x1, y1, z1)
+    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
+    assert actual is True
+
+    cnot = CNOT(1, 0)
+    cnot_circuit = (cnot, cnot)
+    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
+    assert actual is True
+
+    h = H(0)
+    hh_circuit = (h, h)
+    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
+    assert actual is True
+
+    h1 = H(1)
+    xhzh_circuit = (x1, h1, z1, h1)
+    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
+    assert actual is True
+
+    id_only = True
+    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
+    assert actual is True
+    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
+    assert actual is False
+    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
+    assert actual is True
+    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
+    assert actual is True
+
+
+def test_is_scalar_sparse_matrix():
+    np = import_module('numpy')
+    if not np:
+        skip("numpy not installed.")
+
+    scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+    if not scipy:
+        skip("scipy not installed.")
+
+    numqubits = 2
+    id_only = False
+
+    id_gate = (IdentityGate(1),)
+    assert is_scalar_sparse_matrix(id_gate, numqubits, id_only) is True
+
+    x0 = X(0)
+    xx_circuit = (x0, x0)
+    assert is_scalar_sparse_matrix(xx_circuit, numqubits, id_only) is True
+
+    x1 = X(1)
+    y1 = Y(1)
+    xy_circuit = (x1, y1)
+    assert is_scalar_sparse_matrix(xy_circuit, numqubits, id_only) is False
+
+    z1 = Z(1)
+    xyz_circuit = (x1, y1, z1)
+    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is True
+
+    cnot = CNOT(1, 0)
+    cnot_circuit = (cnot, cnot)
+    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True
+
+    h = H(0)
+    hh_circuit = (h, h)
+    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True
+
+    # NOTE:
+    # The elements of the sparse matrix for the following circuit
+    # is actually 1.0000000000000002+0.0j.
+    h1 = H(1)
+    xhzh_circuit = (x1, h1, z1, h1)
+    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True
+
+    id_only = True
+    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True
+    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is False
+    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True
+    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True
+
+
+def test_is_degenerate():
+    (x, y, z, h) = create_gate_sequence()
+
+    gate_id = GateIdentity(x, y, z)
+    ids = {gate_id}
+
+    another_id = (z, y, x)
+    assert is_degenerate(ids, another_id) is True
+
+
+def test_is_reducible():
+    nqubits = 2
+    (x, y, z, h) = create_gate_sequence()
+
+    circuit = (x, y, y)
+    assert is_reducible(circuit, nqubits, 1, 3) is True
+
+    circuit = (x, y, x)
+    assert is_reducible(circuit, nqubits, 1, 3) is False
+
+    circuit = (x, y, y, x)
+    assert is_reducible(circuit, nqubits, 0, 4) is True
+
+    circuit = (x, y, y, x)
+    assert is_reducible(circuit, nqubits, 1, 3) is True
+
+    circuit = (x, y, z, y, y)
+    assert is_reducible(circuit, nqubits, 1, 5) is True
+
+
+def test_bfs_identity_search():
+    assert bfs_identity_search([], 1) == set()
+
+    (x, y, z, h) = create_gate_sequence()
+
+    gate_list = [x]
+    id_set = {GateIdentity(x, x)}
+    assert bfs_identity_search(gate_list, 1, max_depth=2) == id_set
+
+    # Set should not contain degenerate quantum circuits
+    gate_list = [x, y, z]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(x, y, z)}
+    assert bfs_identity_search(gate_list, 1) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(y, z, y, z)}
+    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set
+    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set
+
+    gate_list = [x, y, z, h]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(x, h, z, h),
+                  GateIdentity(y, z, y, z),
+                  GateIdentity(y, h, y, h)}
+    assert bfs_identity_search(gate_list, 1) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h)}
+    assert id_set == bfs_identity_search(gate_list, 1, max_depth=3,
+                                         identity_only=True)
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(x, h, z, h),
+                  GateIdentity(y, z, y, z),
+                  GateIdentity(y, h, y, h),
+                  GateIdentity(x, y, h, x, h),
+                  GateIdentity(x, z, h, y, h),
+                  GateIdentity(y, z, h, z, h)}
+    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, h, z, h)}
+    assert id_set == bfs_identity_search(gate_list, 1, max_depth=4,
+                                         identity_only=True)
+
+    cnot = CNOT(1, 0)
+    gate_list = [x, cnot]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(cnot, cnot),
+                  GateIdentity(x, cnot, x, cnot)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    cgate_x = CGate((1,), x)
+    gate_list = [x, cgate_x]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(cgate_x, cgate_x),
+                  GateIdentity(x, cgate_x, x, cgate_x)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    cgate_z = CGate((0,), Z(1))
+    gate_list = [cnot, cgate_z, h]
+    id_set = {GateIdentity(h, h),
+                  GateIdentity(cgate_z, cgate_z),
+                  GateIdentity(cnot, cnot),
+                  GateIdentity(cnot, h, cgate_z, h)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    s = PhaseGate(0)
+    t = TGate(0)
+    gate_list = [s, t]
+    id_set = {GateIdentity(s, s, s, s)}
+    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set
+
+
+def test_bfs_identity_search_xfail():
+    s = PhaseGate(0)
+    t = TGate(0)
+    gate_list = [Dagger(s), t]
+    id_set = {GateIdentity(Dagger(s), t, t)}
+    assert bfs_identity_search(gate_list, 1, max_depth=3) == id_set

rl/Lib/site-packages/sympy/physics/quantum/tests/test_innerproduct.py

@@ -0,0 +1,71 @@
+from sympy.core.numbers import (I, Integer)
+
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.state import Bra, Ket, StateBase
+
+
+def test_innerproduct():
+    k = Ket('k')
+    b = Bra('b')
+    ip = InnerProduct(b, k)
+    assert isinstance(ip, InnerProduct)
+    assert ip.bra == b
+    assert ip.ket == k
+    assert b*k == InnerProduct(b, k)
+    assert k*(b*k)*b == k*InnerProduct(b, k)*b
+    assert InnerProduct(b, k).subs(b, Dagger(k)) == Dagger(k)*k
+
+
+def test_innerproduct_dagger():
+    k = Ket('k')
+    b = Bra('b')
+    ip = b*k
+    assert Dagger(ip) == Dagger(k)*Dagger(b)
+
+
+class FooState(StateBase):
+    pass
+
+
+class FooKet(Ket, FooState):
+
+    @classmethod
+    def dual_class(self):
+        return FooBra
+
+    def _eval_innerproduct_FooBra(self, bra):
+        return Integer(1)
+
+    def _eval_innerproduct_BarBra(self, bra):
+        return I
+
+
+class FooBra(Bra, FooState):
+    @classmethod
+    def dual_class(self):
+        return FooKet
+
+
+class BarState(StateBase):
+    pass
+
+
+class BarKet(Ket, BarState):
+    @classmethod
+    def dual_class(self):
+        return BarBra
+
+
+class BarBra(Bra, BarState):
+    @classmethod
+    def dual_class(self):
+        return BarKet
+
+
+def test_doit():
+    f = FooKet('foo')
+    b = BarBra('bar')
+    assert InnerProduct(b, f).doit() == I
+    assert InnerProduct(Dagger(f), Dagger(b)).doit() == -I
+    assert InnerProduct(Dagger(f), f).doit() == Integer(1)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_matrixutils.py

@@ -0,0 +1,136 @@
+from sympy.core.random import randint
+
+from sympy.core.numbers import Integer
+from sympy.matrices.dense import (Matrix, ones, zeros)
+
+from sympy.physics.quantum.matrixutils import (
+    to_sympy, to_numpy, to_scipy_sparse, matrix_tensor_product,
+    matrix_to_zero, matrix_zeros, numpy_ndarray, scipy_sparse_matrix
+)
+
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+m = Matrix([[1, 2], [3, 4]])
+
+
+def test_sympy_to_sympy():
+    assert to_sympy(m) == m
+
+
+def test_matrix_to_zero():
+    assert matrix_to_zero(m) == m
+    assert matrix_to_zero(Matrix([[0, 0], [0, 0]])) == Integer(0)
+
+np = import_module('numpy')
+
+
+def test_to_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    result = np.array([[1, 2], [3, 4]], dtype='complex')
+    assert (to_numpy(m) == result).all()
+
+
+def test_matrix_tensor_product():
+    if not np:
+        skip("numpy not installed.")
+
+    l1 = zeros(4)
+    for i in range(16):
+        l1[i] = 2**i
+    l2 = zeros(4)
+    for i in range(16):
+        l2[i] = i
+    l3 = zeros(2)
+    for i in range(4):
+        l3[i] = i
+    vec = Matrix([1, 2, 3])
+
+    #test for Matrix known 4x4 matricies
+    numpyl1 = np.array(l1.tolist())
+    numpyl2 = np.array(l2.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, l2]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [l2, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for other known matrix of different dimensions
+    numpyl2 = np.array(l3.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, l3]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [l3, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for non square matrix
+    numpyl2 = np.array(vec.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, vec]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [vec, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for random matrix with random values that are floats
+    random_matrix1 = np.random.rand(randint(1, 5), randint(1, 5))
+    random_matrix2 = np.random.rand(randint(1, 5), randint(1, 5))
+    numpy_product = np.kron(random_matrix1, random_matrix2)
+    args = [Matrix(random_matrix1.tolist()), Matrix(random_matrix2.tolist())]
+    sympy_product = matrix_tensor_product(*args)
+    assert not (sympy_product - Matrix(numpy_product.tolist())).tolist() > \
+        (ones(sympy_product.rows, sympy_product.cols)*epsilon).tolist()
+
+    #test for three matrix kronecker
+    sympy_product = matrix_tensor_product(l1, vec, l2)
+
+    numpy_product = np.kron(l1, np.kron(vec, l2))
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def test_to_scipy_sparse():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+    else:
+        sparse = scipy.sparse
+
+    result = sparse.csr_matrix([[1, 2], [3, 4]], dtype='complex')
+    assert np.linalg.norm((to_scipy_sparse(m) - result).todense()) == 0.0
+
+epsilon = .000001
+
+
+def test_matrix_zeros_sympy():
+    sym = matrix_zeros(4, 4, format='sympy')
+    assert isinstance(sym, Matrix)
+
+def test_matrix_zeros_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    num = matrix_zeros(4, 4, format='numpy')
+    assert isinstance(num, numpy_ndarray)
+
+def test_matrix_zeros_scipy():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+
+    sci = matrix_zeros(4, 4, format='scipy.sparse')
+    assert isinstance(sci, scipy_sparse_matrix)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_operator.py

@@ -0,0 +1,263 @@
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Integer, pi)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.trigonometric import sin
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.hilbert import HilbertSpace
+from sympy.physics.quantum.operator import (Operator, UnitaryOperator,
+                                            HermitianOperator, OuterProduct,
+                                            DifferentialOperator,
+                                            IdentityOperator)
+from sympy.physics.quantum.state import Ket, Bra, Wavefunction
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.spin import JzKet, JzBra
+from sympy.physics.quantum.trace import Tr
+from sympy.matrices import eye
+
+
+class CustomKet(Ket):
+    @classmethod
+    def default_args(self):
+        return ("t",)
+
+
+class CustomOp(HermitianOperator):
+    @classmethod
+    def default_args(self):
+        return ("T",)
+
+t_ket = CustomKet()
+t_op = CustomOp()
+
+
+def test_operator():
+    A = Operator('A')
+    B = Operator('B')
+    C = Operator('C')
+
+    assert isinstance(A, Operator)
+    assert isinstance(A, QExpr)
+
+    assert A.label == (Symbol('A'),)
+    assert A.is_commutative is False
+    assert A.hilbert_space == HilbertSpace()
+
+    assert A*B != B*A
+
+    assert (A*(B + C)).expand() == A*B + A*C
+    assert ((A + B)**2).expand() == A**2 + A*B + B*A + B**2
+
+    assert t_op.label[0] == Symbol(t_op.default_args()[0])
+
+    assert Operator() == Operator("O")
+    assert A*IdentityOperator() == A
+
+
+def test_operator_inv():
+    A = Operator('A')
+    assert A*A.inv() == 1
+    assert A.inv()*A == 1
+
+
+def test_hermitian():
+    H = HermitianOperator('H')
+
+    assert isinstance(H, HermitianOperator)
+    assert isinstance(H, Operator)
+
+    assert Dagger(H) == H
+    assert H.inv() != H
+    assert H.is_commutative is False
+    assert Dagger(H).is_commutative is False
+
+
+def test_unitary():
+    U = UnitaryOperator('U')
+
+    assert isinstance(U, UnitaryOperator)
+    assert isinstance(U, Operator)
+
+    assert U.inv() == Dagger(U)
+    assert U*Dagger(U) == 1
+    assert Dagger(U)*U == 1
+    assert U.is_commutative is False
+    assert Dagger(U).is_commutative is False
+
+
+def test_identity():
+    I = IdentityOperator()
+    O = Operator('O')
+    x = Symbol("x")
+
+    assert isinstance(I, IdentityOperator)
+    assert isinstance(I, Operator)
+
+    assert I * O == O
+    assert O * I == O
+    assert I * Dagger(O) == Dagger(O)
+    assert Dagger(O) * I == Dagger(O)
+    assert isinstance(I * I, IdentityOperator)
+    assert isinstance(3 * I, Mul)
+    assert isinstance(I * x, Mul)
+    assert I.inv() == I
+    assert Dagger(I) == I
+    assert qapply(I * O) == O
+    assert qapply(O * I) == O
+
+    for n in [2, 3, 5]:
+        assert represent(IdentityOperator(n)) == eye(n)
+
+
+def test_outer_product():
+    k = Ket('k')
+    b = Bra('b')
+    op = OuterProduct(k, b)
+
+    assert isinstance(op, OuterProduct)
+    assert isinstance(op, Operator)
+
+    assert op.ket == k
+    assert op.bra == b
+    assert op.label == (k, b)
+    assert op.is_commutative is False
+
+    op = k*b
+
+    assert isinstance(op, OuterProduct)
+    assert isinstance(op, Operator)
+
+    assert op.ket == k
+    assert op.bra == b
+    assert op.label == (k, b)
+    assert op.is_commutative is False
+
+    op = 2*k*b
+
+    assert op == Mul(Integer(2), k, b)
+
+    op = 2*(k*b)
+
+    assert op == Mul(Integer(2), OuterProduct(k, b))
+
+    assert Dagger(k*b) == OuterProduct(Dagger(b), Dagger(k))
+    assert Dagger(k*b).is_commutative is False
+
+    #test the _eval_trace
+    assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
+
+    # test scaled kets and bras
+    assert OuterProduct(2 * k, b) == 2 * OuterProduct(k, b)
+    assert OuterProduct(k, 2 * b) == 2 * OuterProduct(k, b)
+
+    # test sums of kets and bras
+    k1, k2 = Ket('k1'), Ket('k2')
+    b1, b2 = Bra('b1'), Bra('b2')
+    assert (OuterProduct(k1 + k2, b1) ==
+            OuterProduct(k1, b1) + OuterProduct(k2, b1))
+    assert (OuterProduct(k1, b1 + b2) ==
+            OuterProduct(k1, b1) + OuterProduct(k1, b2))
+    assert (OuterProduct(1 * k1 + 2 * k2, 3 * b1 + 4 * b2) ==
+            3 * OuterProduct(k1, b1) +
+            4 * OuterProduct(k1, b2) +
+            6 * OuterProduct(k2, b1) +
+            8 * OuterProduct(k2, b2))
+
+
+def test_operator_dagger():
+    A = Operator('A')
+    B = Operator('B')
+    assert Dagger(A*B) == Dagger(B)*Dagger(A)
+    assert Dagger(A + B) == Dagger(A) + Dagger(B)
+    assert Dagger(A**2) == Dagger(A)**2
+
+
+def test_differential_operator():
+    x = Symbol('x')
+    f = Function('f')
+    d = DifferentialOperator(Derivative(f(x), x), f(x))
+    g = Wavefunction(x**2, x)
+    assert qapply(d*g) == Wavefunction(2*x, x)
+    assert d.expr == Derivative(f(x), x)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 2), f(x))
+
+    d = DifferentialOperator(Derivative(f(x), x, 2), f(x))
+    g = Wavefunction(x**3, x)
+    assert qapply(d*g) == Wavefunction(6*x, x)
+    assert d.expr == Derivative(f(x), x, 2)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 3), f(x))
+
+    d = DifferentialOperator(1/x*Derivative(f(x), x), f(x))
+    assert d.expr == 1/x*Derivative(f(x), x)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == \
+        DifferentialOperator(Derivative(1/x*Derivative(f(x), x), x), f(x))
+    assert qapply(d*g) == Wavefunction(3*x, x)
+
+    # 2D cartesian Laplacian
+    y = Symbol('y')
+    d = DifferentialOperator(Derivative(f(x, y), x, 2) +
+                             Derivative(f(x, y), y, 2), f(x, y))
+    w = Wavefunction(x**3*y**2 + y**3*x**2, x, y)
+    assert d.expr == Derivative(f(x, y), x, 2) + Derivative(f(x, y), y, 2)
+    assert d.function == f(x, y)
+    assert d.variables == (x, y)
+    assert diff(d, x) == \
+        DifferentialOperator(Derivative(d.expr, x), f(x, y))
+    assert diff(d, y) == \
+        DifferentialOperator(Derivative(d.expr, y), f(x, y))
+    assert qapply(d*w) == Wavefunction(2*x**3 + 6*x*y**2 + 6*x**2*y + 2*y**3,
+                                       x, y)
+
+    # 2D polar Laplacian (th = theta)
+    r, th = symbols('r th')
+    d = DifferentialOperator(1/r*Derivative(r*Derivative(f(r, th), r), r) +
+                             1/(r**2)*Derivative(f(r, th), th, 2), f(r, th))
+    w = Wavefunction(r**2*sin(th), r, (th, 0, pi))
+    assert d.expr == \
+        1/r*Derivative(r*Derivative(f(r, th), r), r) + \
+        1/(r**2)*Derivative(f(r, th), th, 2)
+    assert d.function == f(r, th)
+    assert d.variables == (r, th)
+    assert diff(d, r) == \
+        DifferentialOperator(Derivative(d.expr, r), f(r, th))
+    assert diff(d, th) == \
+        DifferentialOperator(Derivative(d.expr, th), f(r, th))
+    assert qapply(d*w) == Wavefunction(3*sin(th), r, (th, 0, pi))
+
+
+def test_eval_power():
+    from sympy.core import Pow
+    from sympy.core.expr import unchanged
+    O = Operator('O')
+    U = UnitaryOperator('U')
+    H = HermitianOperator('H')
+    assert O**-1 == O.inv() # same as doc test
+    assert U**-1 == U.inv()
+    assert H**-1 == H.inv()
+    x = symbols("x", commutative = True)
+    assert unchanged(Pow, H, x) # verify Pow(H,x)=="X^n"
+    assert H**x == Pow(H, x)
+    assert Pow(H,x) == Pow(H, x, evaluate=False) # Just check
+    from sympy.physics.quantum.gate import XGate
+    X = XGate(0) # is hermitian and unitary
+    assert unchanged(Pow, X, x) # verify Pow(X,x)=="X^x"
+    assert X**x == Pow(X, x)
+    assert Pow(X, x, evaluate=False) == Pow(X, x) # Just check
+    n = symbols("n", integer=True, even=True)
+    assert X**n == 1
+    n = symbols("n", integer=True, odd=True)
+    assert X**n == X
+    n = symbols("n", integer=True)
+    assert unchanged(Pow, X, n) # verify Pow(X,n)=="X^n"
+    assert X**n == Pow(X, n)
+    assert Pow(X, n, evaluate=False)==Pow(X, n) # Just check
+    assert X**4 == 1
+    assert X**7 == X

rl/Lib/site-packages/sympy/physics/quantum/tests/test_operatorordering.py

@@ -0,0 +1,50 @@
+from sympy.physics.quantum import Dagger
+from sympy.physics.quantum.boson import BosonOp
+from sympy.physics.quantum.fermion import FermionOp
+from sympy.physics.quantum.operatorordering import (normal_order,
+                                                 normal_ordered_form)
+
+
+def test_normal_order():
+    a = BosonOp('a')
+
+    c = FermionOp('c')
+
+    assert normal_order(a * Dagger(a)) == Dagger(a) * a
+    assert normal_order(Dagger(a) * a) == Dagger(a) * a
+    assert normal_order(a * Dagger(a) ** 2) == Dagger(a) ** 2 * a
+
+    assert normal_order(c * Dagger(c)) == - Dagger(c) * c
+    assert normal_order(Dagger(c) * c) == Dagger(c) * c
+    assert normal_order(c * Dagger(c) ** 2) == Dagger(c) ** 2 * c
+
+
+def test_normal_ordered_form():
+    a = BosonOp('a')
+    b = BosonOp('b')
+
+    c = FermionOp('c')
+    d = FermionOp('d')
+
+    assert normal_ordered_form(Dagger(a) * a) == Dagger(a) * a
+    assert normal_ordered_form(a * Dagger(a)) == 1 + Dagger(a) * a
+    assert normal_ordered_form(a ** 2 * Dagger(a)) == \
+        2 * a + Dagger(a) * a ** 2
+    assert normal_ordered_form(a ** 3 * Dagger(a)) == \
+        3 * a ** 2 + Dagger(a) * a ** 3
+
+    assert normal_ordered_form(Dagger(c) * c) == Dagger(c) * c
+    assert normal_ordered_form(c * Dagger(c)) == 1 - Dagger(c) * c
+    assert normal_ordered_form(c ** 2 * Dagger(c)) == Dagger(c) * c ** 2
+    assert normal_ordered_form(c ** 3 * Dagger(c)) == \
+        c ** 2 - Dagger(c) * c ** 3
+
+    assert normal_ordered_form(a * Dagger(b), True) == Dagger(b) * a
+    assert normal_ordered_form(Dagger(a) * b, True) == Dagger(a) * b
+    assert normal_ordered_form(b * a, True) == a * b
+    assert normal_ordered_form(Dagger(b) * Dagger(a), True) == Dagger(a) * Dagger(b)
+
+    assert normal_ordered_form(c * Dagger(d), True) == -Dagger(d) * c
+    assert normal_ordered_form(Dagger(c) * d, True) == Dagger(c) * d
+    assert normal_ordered_form(d * c, True) == -c * d
+    assert normal_ordered_form(Dagger(d) * Dagger(c), True) == -Dagger(c) * Dagger(d)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_operatorset.py

@@ -0,0 +1,68 @@
+from sympy.core.singleton import S
+
+from sympy.physics.quantum.operatorset import (
+    operators_to_state, state_to_operators
+)
+
+from sympy.physics.quantum.cartesian import (
+    XOp, XKet, PxOp, PxKet, XBra, PxBra
+)
+
+from sympy.physics.quantum.state import Ket, Bra
+from sympy.physics.quantum.operator import Operator
+from sympy.physics.quantum.spin import (
+    JxKet, JyKet, JzKet, JxBra, JyBra, JzBra,
+    JxOp, JyOp, JzOp, J2Op
+)
+
+from sympy.testing.pytest import raises
+
+
+def test_spin():
+    assert operators_to_state({J2Op, JxOp}) == JxKet
+    assert operators_to_state({J2Op, JyOp}) == JyKet
+    assert operators_to_state({J2Op, JzOp}) == JzKet
+    assert operators_to_state({J2Op(), JxOp()}) == JxKet
+    assert operators_to_state({J2Op(), JyOp()}) == JyKet
+    assert operators_to_state({J2Op(), JzOp()}) == JzKet
+
+    assert state_to_operators(JxKet) == {J2Op, JxOp}
+    assert state_to_operators(JyKet) == {J2Op, JyOp}
+    assert state_to_operators(JzKet) == {J2Op, JzOp}
+    assert state_to_operators(JxBra) == {J2Op, JxOp}
+    assert state_to_operators(JyBra) == {J2Op, JyOp}
+    assert state_to_operators(JzBra) == {J2Op, JzOp}
+
+    assert state_to_operators(JxKet(S.Half, S.Half)) == {J2Op(), JxOp()}
+    assert state_to_operators(JyKet(S.Half, S.Half)) == {J2Op(), JyOp()}
+    assert state_to_operators(JzKet(S.Half, S.Half)) == {J2Op(), JzOp()}
+    assert state_to_operators(JxBra(S.Half, S.Half)) == {J2Op(), JxOp()}
+    assert state_to_operators(JyBra(S.Half, S.Half)) == {J2Op(), JyOp()}
+    assert state_to_operators(JzBra(S.Half, S.Half)) == {J2Op(), JzOp()}
+
+
+def test_op_to_state():
+    assert operators_to_state(XOp) == XKet()
+    assert operators_to_state(PxOp) == PxKet()
+    assert operators_to_state(Operator) == Ket()
+
+    assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
+    assert state_to_operators(operators_to_state(XOp())) == XOp()
+
+    raises(NotImplementedError, lambda: operators_to_state(XKet))
+
+
+def test_state_to_op():
+    assert state_to_operators(XKet) == XOp()
+    assert state_to_operators(PxKet) == PxOp()
+    assert state_to_operators(XBra) == XOp()
+    assert state_to_operators(PxBra) == PxOp()
+    assert state_to_operators(Ket) == Operator()
+    assert state_to_operators(Bra) == Operator()
+
+    assert operators_to_state(state_to_operators(XKet("test"))) == XKet("test")
+    assert operators_to_state(state_to_operators(XBra("test"))) == XKet("test")
+    assert operators_to_state(state_to_operators(XKet())) == XKet()
+    assert operators_to_state(state_to_operators(XBra())) == XKet()
+
+    raises(NotImplementedError, lambda: state_to_operators(XOp))

rl/Lib/site-packages/sympy/physics/quantum/tests/test_pauli.py

@@ -0,0 +1,159 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.matrices.dense import Matrix
+from sympy.printing.latex import latex
+from sympy.physics.quantum import (Dagger, Commutator, AntiCommutator, qapply,
+                                   Operator, represent)
+from sympy.physics.quantum.pauli import (SigmaOpBase, SigmaX, SigmaY, SigmaZ,
+                                         SigmaMinus, SigmaPlus,
+                                         qsimplify_pauli)
+from sympy.physics.quantum.pauli import SigmaZKet, SigmaZBra
+from sympy.testing.pytest import raises
+
+
+sx, sy, sz = SigmaX(), SigmaY(), SigmaZ()
+sx1, sy1, sz1 = SigmaX(1), SigmaY(1), SigmaZ(1)
+sx2, sy2, sz2 = SigmaX(2), SigmaY(2), SigmaZ(2)
+
+sm, sp = SigmaMinus(), SigmaPlus()
+sm1, sp1 = SigmaMinus(1), SigmaPlus(1)
+A, B = Operator("A"), Operator("B")
+
+
+def test_pauli_operators_types():
+
+    assert isinstance(sx, SigmaOpBase) and isinstance(sx, SigmaX)
+    assert isinstance(sy, SigmaOpBase) and isinstance(sy, SigmaY)
+    assert isinstance(sz, SigmaOpBase) and isinstance(sz, SigmaZ)
+    assert isinstance(sm, SigmaOpBase) and isinstance(sm, SigmaMinus)
+    assert isinstance(sp, SigmaOpBase) and isinstance(sp, SigmaPlus)
+
+
+def test_pauli_operators_commutator():
+
+    assert Commutator(sx, sy).doit() == 2 * I * sz
+    assert Commutator(sy, sz).doit() == 2 * I * sx
+    assert Commutator(sz, sx).doit() == 2 * I * sy
+
+
+def test_pauli_operators_commutator_with_labels():
+
+    assert Commutator(sx1, sy1).doit() == 2 * I * sz1
+    assert Commutator(sy1, sz1).doit() == 2 * I * sx1
+    assert Commutator(sz1, sx1).doit() == 2 * I * sy1
+
+    assert Commutator(sx2, sy2).doit() == 2 * I * sz2
+    assert Commutator(sy2, sz2).doit() == 2 * I * sx2
+    assert Commutator(sz2, sx2).doit() == 2 * I * sy2
+
+    assert Commutator(sx1, sy2).doit() == 0
+    assert Commutator(sy1, sz2).doit() == 0
+    assert Commutator(sz1, sx2).doit() == 0
+
+
+def test_pauli_operators_anticommutator():
+
+    assert AntiCommutator(sy, sz).doit() == 0
+    assert AntiCommutator(sz, sx).doit() == 0
+    assert AntiCommutator(sx, sm).doit() == 1
+    assert AntiCommutator(sx, sp).doit() == 1
+
+
+def test_pauli_operators_adjoint():
+
+    assert Dagger(sx) == sx
+    assert Dagger(sy) == sy
+    assert Dagger(sz) == sz
+
+
+def test_pauli_operators_adjoint_with_labels():
+
+    assert Dagger(sx1) == sx1
+    assert Dagger(sy1) == sy1
+    assert Dagger(sz1) == sz1
+
+    assert Dagger(sx1) != sx2
+    assert Dagger(sy1) != sy2
+    assert Dagger(sz1) != sz2
+
+
+def test_pauli_operators_multiplication():
+
+    assert qsimplify_pauli(sx * sx) == 1
+    assert qsimplify_pauli(sy * sy) == 1
+    assert qsimplify_pauli(sz * sz) == 1
+
+    assert qsimplify_pauli(sx * sy) == I * sz
+    assert qsimplify_pauli(sy * sz) == I * sx
+    assert qsimplify_pauli(sz * sx) == I * sy
+
+    assert qsimplify_pauli(sy * sx) == - I * sz
+    assert qsimplify_pauli(sz * sy) == - I * sx
+    assert qsimplify_pauli(sx * sz) == - I * sy
+
+
+def test_pauli_operators_multiplication_with_labels():
+
+    assert qsimplify_pauli(sx1 * sx1) == 1
+    assert qsimplify_pauli(sy1 * sy1) == 1
+    assert qsimplify_pauli(sz1 * sz1) == 1
+
+    assert isinstance(sx1 * sx2, Mul)
+    assert isinstance(sy1 * sy2, Mul)
+    assert isinstance(sz1 * sz2, Mul)
+
+    assert qsimplify_pauli(sx1 * sy1 * sx2 * sy2) == - sz1 * sz2
+    assert qsimplify_pauli(sy1 * sz1 * sz2 * sx2) == - sx1 * sy2
+
+
+def test_pauli_states():
+    sx, sz = SigmaX(), SigmaZ()
+
+    up = SigmaZKet(0)
+    down = SigmaZKet(1)
+
+    assert qapply(sx * up) == down
+    assert qapply(sx * down) == up
+    assert qapply(sz * up) == up
+    assert qapply(sz * down) == - down
+
+    up = SigmaZBra(0)
+    down = SigmaZBra(1)
+
+    assert qapply(up * sx, dagger=True) == down
+    assert qapply(down * sx, dagger=True) == up
+    assert qapply(up * sz, dagger=True) == up
+    assert qapply(down * sz, dagger=True) == - down
+
+    assert Dagger(SigmaZKet(0)) == SigmaZBra(0)
+    assert Dagger(SigmaZBra(1)) == SigmaZKet(1)
+    raises(ValueError, lambda: SigmaZBra(2))
+    raises(ValueError, lambda: SigmaZKet(2))
+
+
+def test_use_name():
+    assert sm.use_name is False
+    assert sm1.use_name is True
+    assert sx.use_name is False
+    assert sx1.use_name is True
+
+
+def test_printing():
+    assert latex(sx) == r'{\sigma_x}'
+    assert latex(sx1) == r'{\sigma_x^{(1)}}'
+    assert latex(sy) == r'{\sigma_y}'
+    assert latex(sy1) == r'{\sigma_y^{(1)}}'
+    assert latex(sz) == r'{\sigma_z}'
+    assert latex(sz1) == r'{\sigma_z^{(1)}}'
+    assert latex(sm) == r'{\sigma_-}'
+    assert latex(sm1) == r'{\sigma_-^{(1)}}'
+    assert latex(sp) == r'{\sigma_+}'
+    assert latex(sp1) == r'{\sigma_+^{(1)}}'
+
+
+def test_represent():
+    assert represent(sx) == Matrix([[0, 1], [1, 0]])
+    assert represent(sy) == Matrix([[0, -I], [I, 0]])
+    assert represent(sz) == Matrix([[1, 0], [0, -1]])
+    assert represent(sm) == Matrix([[0, 0], [1, 0]])
+    assert represent(sp) == Matrix([[0, 1], [0, 0]])

rl/Lib/site-packages/sympy/physics/quantum/tests/test_piab.py

@@ -0,0 +1,29 @@
+"""Tests for piab.py"""
+
+from sympy.core.numbers import pi
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.sets.sets import Interval
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.physics.quantum import L2, qapply, hbar, represent
+from sympy.physics.quantum.piab import PIABHamiltonian, PIABKet, PIABBra, m, L
+
+i, j, n, x = symbols('i j n x')
+
+
+def test_H():
+    assert PIABHamiltonian('H').hilbert_space == \
+        L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert qapply(PIABHamiltonian('H')*PIABKet(n)) == \
+        (n**2*pi**2*hbar**2)/(2*m*L**2)*PIABKet(n)
+
+
+def test_states():
+    assert PIABKet(n).dual_class() == PIABBra
+    assert PIABKet(n).hilbert_space == \
+        L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert represent(PIABKet(n)) == sqrt(2/L)*sin(n*pi*x/L)
+    assert (PIABBra(i)*PIABKet(j)).doit() == KroneckerDelta(i, j)
+    assert PIABBra(n).dual_class() == PIABKet

rl/Lib/site-packages/sympy/physics/quantum/tests/test_printing.py

@@ -0,0 +1,900 @@
+# -*- encoding: utf-8 -*-
+"""
+TODO:
+* Address Issue 2251, printing of spin states
+"""
+from __future__ import annotations
+from typing import Any
+
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.cg import CG, Wigner3j, Wigner6j, Wigner9j
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.constants import hbar
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.gate import CGate, CNotGate, IdentityGate, UGate, XGate
+from sympy.physics.quantum.hilbert import ComplexSpace, FockSpace, HilbertSpace, L2
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.operator import Operator, OuterProduct, DifferentialOperator
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.qubit import Qubit, IntQubit
+from sympy.physics.quantum.spin import Jz, J2, JzBra, JzBraCoupled, JzKet, JzKetCoupled, Rotation, WignerD
+from sympy.physics.quantum.state import Bra, Ket, TimeDepBra, TimeDepKet
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.sho1d import RaisingOp
+
+from sympy.core.function import (Derivative, Function)
+from sympy.core.numbers import oo
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.matrices.dense import Matrix
+from sympy.sets.sets import Interval
+from sympy.testing.pytest import XFAIL
+
+# Imports used in srepr strings
+from sympy.physics.quantum.spin import JzOp
+
+from sympy.printing import srepr
+from sympy.printing.pretty import pretty as xpretty
+from sympy.printing.latex import latex
+
+MutableDenseMatrix = Matrix
+
+
+ENV: dict[str, Any] = {}
+exec('from sympy import *', ENV)
+exec('from sympy.physics.quantum import *', ENV)
+exec('from sympy.physics.quantum.cg import *', ENV)
+exec('from sympy.physics.quantum.spin import *', ENV)
+exec('from sympy.physics.quantum.hilbert import *', ENV)
+exec('from sympy.physics.quantum.qubit import *', ENV)
+exec('from sympy.physics.quantum.qexpr import *', ENV)
+exec('from sympy.physics.quantum.gate import *', ENV)
+exec('from sympy.physics.quantum.constants import *', ENV)
+
+
+def sT(expr, string):
+    """
+    sT := sreprTest
+    from sympy/printing/tests/test_repr.py
+    """
+    assert srepr(expr) == string
+    assert eval(string, ENV) == expr
+
+
+def pretty(expr):
+    """ASCII pretty-printing"""
+    return xpretty(expr, use_unicode=False, wrap_line=False)
+
+
+def upretty(expr):
+    """Unicode pretty-printing"""
+    return xpretty(expr, use_unicode=True, wrap_line=False)
+
+
+def test_anticommutator():
+    A = Operator('A')
+    B = Operator('B')
+    ac = AntiCommutator(A, B)
+    ac_tall = AntiCommutator(A**2, B)
+    assert str(ac) == '{A,B}'
+    assert pretty(ac) == '{A,B}'
+    assert upretty(ac) == '{A,B}'
+    assert latex(ac) == r'\left\{A,B\right\}'
+    sT(ac, "AntiCommutator(Operator(Symbol('A')),Operator(Symbol('B')))")
+    assert str(ac_tall) == '{A**2,B}'
+    ascii_str = \
+"""\
+/ 2  \\\n\
+<A ,B>\n\
+\\    /\
+"""
+    ucode_str = \
+"""\
+⎧ 2  ⎫\n\
+⎨A ,B⎬\n\
+⎩    ⎭\
+"""
+    assert pretty(ac_tall) == ascii_str
+    assert upretty(ac_tall) == ucode_str
+    assert latex(ac_tall) == r'\left\{A^{2},B\right\}'
+    sT(ac_tall, "AntiCommutator(Pow(Operator(Symbol('A')), Integer(2)),Operator(Symbol('B')))")
+
+
+def test_cg():
+    cg = CG(1, 2, 3, 4, 5, 6)
+    wigner3j = Wigner3j(1, 2, 3, 4, 5, 6)
+    wigner6j = Wigner6j(1, 2, 3, 4, 5, 6)
+    wigner9j = Wigner9j(1, 2, 3, 4, 5, 6, 7, 8, 9)
+    assert str(cg) == 'CG(1, 2, 3, 4, 5, 6)'
+    ascii_str = \
+"""\
+ 5,6    \n\
+C       \n\
+ 1,2,3,4\
+"""
+    ucode_str = \
+"""\
+ 5,6    \n\
+C       \n\
+ 1,2,3,4\
+"""
+    assert pretty(cg) == ascii_str
+    assert upretty(cg) == ucode_str
+    assert latex(cg) == 'C^{5,6}_{1,2,3,4}'
+    assert latex(cg ** 2) == R'\left(C^{5,6}_{1,2,3,4}\right)^{2}'
+    sT(cg, "CG(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))")
+    assert str(wigner3j) == 'Wigner3j(1, 2, 3, 4, 5, 6)'
+    ascii_str = \
+"""\
+/1  3  5\\\n\
+|       |\n\
+\\2  4  6/\
+"""
+    ucode_str = \
+"""\
+⎛1  3  5⎞\n\
+⎜       ⎟\n\
+⎝2  4  6⎠\
+"""
+    assert pretty(wigner3j) == ascii_str
+    assert upretty(wigner3j) == ucode_str
+    assert latex(wigner3j) == \
+        r'\left(\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 4 & 6 \end{array}\right)'
+    sT(wigner3j, "Wigner3j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))")
+    assert str(wigner6j) == 'Wigner6j(1, 2, 3, 4, 5, 6)'
+    ascii_str = \
+"""\
+/1  2  3\\\n\
+<       >\n\
+\\4  5  6/\
+"""
+    ucode_str = \
+"""\
+⎧1  2  3⎫\n\
+⎨       ⎬\n\
+⎩4  5  6⎭\
+"""
+    assert pretty(wigner6j) == ascii_str
+    assert upretty(wigner6j) == ucode_str
+    assert latex(wigner6j) == \
+        r'\left\{\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right\}'
+    sT(wigner6j, "Wigner6j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))")
+    assert str(wigner9j) == 'Wigner9j(1, 2, 3, 4, 5, 6, 7, 8, 9)'
+    ascii_str = \
+"""\
+/1  2  3\\\n\
+|       |\n\
+<4  5  6>\n\
+|       |\n\
+\\7  8  9/\
+"""
+    ucode_str = \
+"""\
+⎧1  2  3⎫\n\
+⎪       ⎪\n\
+⎨4  5  6⎬\n\
+⎪       ⎪\n\
+⎩7  8  9⎭\
+"""
+    assert pretty(wigner9j) == ascii_str
+    assert upretty(wigner9j) == ucode_str
+    assert latex(wigner9j) == \
+        r'\left\{\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right\}'
+    sT(wigner9j, "Wigner9j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6), Integer(7), Integer(8), Integer(9))")
+
+
+def test_commutator():
+    A = Operator('A')
+    B = Operator('B')
+    c = Commutator(A, B)
+    c_tall = Commutator(A**2, B)
+    assert str(c) == '[A,B]'
+    assert pretty(c) == '[A,B]'
+    assert upretty(c) == '[A,B]'
+    assert latex(c) == r'\left[A,B\right]'
+    sT(c, "Commutator(Operator(Symbol('A')),Operator(Symbol('B')))")
+    assert str(c_tall) == '[A**2,B]'
+    ascii_str = \
+"""\
+[ 2  ]\n\
+[A ,B]\
+"""
+    ucode_str = \
+"""\
+⎡ 2  ⎤\n\
+⎣A ,B⎦\
+"""
+    assert pretty(c_tall) == ascii_str
+    assert upretty(c_tall) == ucode_str
+    assert latex(c_tall) == r'\left[A^{2},B\right]'
+    sT(c_tall, "Commutator(Pow(Operator(Symbol('A')), Integer(2)),Operator(Symbol('B')))")
+
+
+def test_constants():
+    assert str(hbar) == 'hbar'
+    assert pretty(hbar) == 'hbar'
+    assert upretty(hbar) == 'ℏ'
+    assert latex(hbar) == r'\hbar'
+    sT(hbar, "HBar()")
+
+
+def test_dagger():
+    x = symbols('x')
+    expr = Dagger(x)
+    assert str(expr) == 'Dagger(x)'
+    ascii_str = \
+"""\
+ +\n\
+x \
+"""
+    ucode_str = \
+"""\
+ †\n\
+x \
+"""
+    assert pretty(expr) == ascii_str
+    assert upretty(expr) == ucode_str
+    assert latex(expr) == r'x^{\dagger}'
+    sT(expr, "Dagger(Symbol('x'))")
+
+
+@XFAIL
+def test_gate_failing():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+    g = UGate((0,), uMat)
+    assert str(g) == 'U(0)'
+
+
+def test_gate():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+    q = Qubit(1, 0, 1, 0, 1)
+    g1 = IdentityGate(2)
+    g2 = CGate((3, 0), XGate(1))
+    g3 = CNotGate(1, 0)
+    g4 = UGate((0,), uMat)
+    assert str(g1) == '1(2)'
+    assert pretty(g1) == '1 \n 2'
+    assert upretty(g1) == '1 \n 2'
+    assert latex(g1) == r'1_{2}'
+    sT(g1, "IdentityGate(Integer(2))")
+    assert str(g1*q) == '1(2)*|10101>'
+    ascii_str = \
+"""\
+1 *|10101>\n\
+ 2        \
+"""
+    ucode_str = \
+"""\
+1 ⋅❘10101⟩\n\
+ 2        \
+"""
+    assert pretty(g1*q) == ascii_str
+    assert upretty(g1*q) == ucode_str
+    assert latex(g1*q) == r'1_{2} {\left|10101\right\rangle }'
+    sT(g1*q, "Mul(IdentityGate(Integer(2)), Qubit(Integer(1),Integer(0),Integer(1),Integer(0),Integer(1)))")
+    assert str(g2) == 'C((3,0),X(1))'
+    ascii_str = \
+"""\
+C   /X \\\n\
+ 3,0\\ 1/\
+"""
+    ucode_str = \
+"""\
+C   ⎛X ⎞\n\
+ 3,0⎝ 1⎠\
+"""
+    assert pretty(g2) == ascii_str
+    assert upretty(g2) == ucode_str
+    assert latex(g2) == r'C_{3,0}{\left(X_{1}\right)}'
+    sT(g2, "CGate(Tuple(Integer(3), Integer(0)),XGate(Integer(1)))")
+    assert str(g3) == 'CNOT(1,0)'
+    ascii_str = \
+"""\
+CNOT   \n\
+    1,0\
+"""
+    ucode_str = \
+"""\
+CNOT   \n\
+    1,0\
+"""
+    assert pretty(g3) == ascii_str
+    assert upretty(g3) == ucode_str
+    assert latex(g3) == r'\text{CNOT}_{1,0}'
+    sT(g3, "CNotGate(Integer(1),Integer(0))")
+    ascii_str = \
+"""\
+U \n\
+ 0\
+"""
+    ucode_str = \
+"""\
+U \n\
+ 0\
+"""
+    assert str(g4) == \
+"""\
+U((0,),Matrix([\n\
+[a, b],\n\
+[c, d]]))\
+"""
+    assert pretty(g4) == ascii_str
+    assert upretty(g4) == ucode_str
+    assert latex(g4) == r'U_{0}'
+    sT(g4, "UGate(Tuple(Integer(0)),ImmutableDenseMatrix([[Symbol('a'), Symbol('b')], [Symbol('c'), Symbol('d')]]))")
+
+
+def test_hilbert():
+    h1 = HilbertSpace()
+    h2 = ComplexSpace(2)
+    h3 = FockSpace()
+    h4 = L2(Interval(0, oo))
+    assert str(h1) == 'H'
+    assert pretty(h1) == 'H'
+    assert upretty(h1) == 'H'
+    assert latex(h1) == r'\mathcal{H}'
+    sT(h1, "HilbertSpace()")
+    assert str(h2) == 'C(2)'
+    ascii_str = \
+"""\
+ 2\n\
+C \
+"""
+    ucode_str = \
+"""\
+ 2\n\
+C \
+"""
+    assert pretty(h2) == ascii_str
+    assert upretty(h2) == ucode_str
+    assert latex(h2) == r'\mathcal{C}^{2}'
+    sT(h2, "ComplexSpace(Integer(2))")
+    assert str(h3) == 'F'
+    assert pretty(h3) == 'F'
+    assert upretty(h3) == 'F'
+    assert latex(h3) == r'\mathcal{F}'
+    sT(h3, "FockSpace()")
+    assert str(h4) == 'L2(Interval(0, oo))'
+    ascii_str = \
+"""\
+ 2\n\
+L \
+"""
+    ucode_str = \
+"""\
+ 2\n\
+L \
+"""
+    assert pretty(h4) == ascii_str
+    assert upretty(h4) == ucode_str
+    assert latex(h4) == r'{\mathcal{L}^2}\left( \left[0, \infty\right) \right)'
+    sT(h4, "L2(Interval(Integer(0), oo, false, true))")
+    assert str(h1 + h2) == 'H+C(2)'
+    ascii_str = \
+"""\
+     2\n\
+H + C \
+"""
+    ucode_str = \
+"""\
+     2\n\
+H ⊕ C \
+"""
+    assert pretty(h1 + h2) == ascii_str
+    assert upretty(h1 + h2) == ucode_str
+    assert latex(h1 + h2)
+    sT(h1 + h2, "DirectSumHilbertSpace(HilbertSpace(),ComplexSpace(Integer(2)))")
+    assert str(h1*h2) == "H*C(2)"
+    ascii_str = \
+"""\
+     2\n\
+H x C \
+"""
+    ucode_str = \
+"""\
+     2\n\
+H ⨂ C \
+"""
+    assert pretty(h1*h2) == ascii_str
+    assert upretty(h1*h2) == ucode_str
+    assert latex(h1*h2)
+    sT(h1*h2,
+       "TensorProductHilbertSpace(HilbertSpace(),ComplexSpace(Integer(2)))")
+    assert str(h1**2) == 'H**2'
+    ascii_str = \
+"""\
+ x2\n\
+H  \
+"""
+    ucode_str = \
+"""\
+ ⨂2\n\
+H  \
+"""
+    assert pretty(h1**2) == ascii_str
+    assert upretty(h1**2) == ucode_str
+    assert latex(h1**2) == r'{\mathcal{H}}^{\otimes 2}'
+    sT(h1**2, "TensorPowerHilbertSpace(HilbertSpace(),Integer(2))")
+
+
+def test_innerproduct():
+    x = symbols('x')
+    ip1 = InnerProduct(Bra(), Ket())
+    ip2 = InnerProduct(TimeDepBra(), TimeDepKet())
+    ip3 = InnerProduct(JzBra(1, 1), JzKet(1, 1))
+    ip4 = InnerProduct(JzBraCoupled(1, 1, (1, 1)), JzKetCoupled(1, 1, (1, 1)))
+    ip_tall1 = InnerProduct(Bra(x/2), Ket(x/2))
+    ip_tall2 = InnerProduct(Bra(x), Ket(x/2))
+    ip_tall3 = InnerProduct(Bra(x/2), Ket(x))
+    assert str(ip1) == '<psi|psi>'
+    assert pretty(ip1) == '<psi|psi>'
+    assert upretty(ip1) == '⟨ψ❘ψ⟩'
+    assert latex(
+        ip1) == r'\left\langle \psi \right. {\left|\psi\right\rangle }'
+    sT(ip1, "InnerProduct(Bra(Symbol('psi')),Ket(Symbol('psi')))")
+    assert str(ip2) == '<psi;t|psi;t>'
+    assert pretty(ip2) == '<psi;t|psi;t>'
+    assert upretty(ip2) == '⟨ψ;t❘ψ;t⟩'
+    assert latex(ip2) == \
+        r'\left\langle \psi;t \right. {\left|\psi;t\right\rangle }'
+    sT(ip2, "InnerProduct(TimeDepBra(Symbol('psi'),Symbol('t')),TimeDepKet(Symbol('psi'),Symbol('t')))")
+    assert str(ip3) == "<1,1|1,1>"
+    assert pretty(ip3) == '<1,1|1,1>'
+    assert upretty(ip3) == '⟨1,1❘1,1⟩'
+    assert latex(ip3) == r'\left\langle 1,1 \right. {\left|1,1\right\rangle }'
+    sT(ip3, "InnerProduct(JzBra(Integer(1),Integer(1)),JzKet(Integer(1),Integer(1)))")
+    assert str(ip4) == "<1,1,j1=1,j2=1|1,1,j1=1,j2=1>"
+    assert pretty(ip4) == '<1,1,j1=1,j2=1|1,1,j1=1,j2=1>'
+    assert upretty(ip4) == '⟨1,1,j₁=1,j₂=1❘1,1,j₁=1,j₂=1⟩'
+    assert latex(ip4) == \
+        r'\left\langle 1,1,j_{1}=1,j_{2}=1 \right. {\left|1,1,j_{1}=1,j_{2}=1\right\rangle }'
+    sT(ip4, "InnerProduct(JzBraCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))),JzKetCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))))")
+    assert str(ip_tall1) == '<x/2|x/2>'
+    ascii_str = \
+"""\
+ / | \\ \n\
+/ x|x \\\n\
+\\ -|- /\n\
+ \\2|2/ \
+"""
+    ucode_str = \
+"""\
+ ╱ │ ╲ \n\
+╱ x│x ╲\n\
+╲ ─│─ ╱\n\
+ ╲2│2╱ \
+"""
+    assert pretty(ip_tall1) == ascii_str
+    assert upretty(ip_tall1) == ucode_str
+    assert latex(ip_tall1) == \
+        r'\left\langle \frac{x}{2} \right. {\left|\frac{x}{2}\right\rangle }'
+    sT(ip_tall1, "InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Mul(Rational(1, 2), Symbol('x'))))")
+    assert str(ip_tall2) == '<x|x/2>'
+    ascii_str = \
+"""\
+ / | \\ \n\
+/  |x \\\n\
+\\ x|- /\n\
+ \\ |2/ \
+"""
+    ucode_str = \
+"""\
+ ╱ │ ╲ \n\
+╱  │x ╲\n\
+╲ x│─ ╱\n\
+ ╲ │2╱ \
+"""
+    assert pretty(ip_tall2) == ascii_str
+    assert upretty(ip_tall2) == ucode_str
+    assert latex(ip_tall2) == \
+        r'\left\langle x \right. {\left|\frac{x}{2}\right\rangle }'
+    sT(ip_tall2,
+       "InnerProduct(Bra(Symbol('x')),Ket(Mul(Rational(1, 2), Symbol('x'))))")
+    assert str(ip_tall3) == '<x/2|x>'
+    ascii_str = \
+"""\
+ / | \\ \n\
+/ x|  \\\n\
+\\ -|x /\n\
+ \\2| / \
+"""
+    ucode_str = \
+"""\
+ ╱ │ ╲ \n\
+╱ x│  ╲\n\
+╲ ─│x ╱\n\
+ ╲2│ ╱ \
+"""
+    assert pretty(ip_tall3) == ascii_str
+    assert upretty(ip_tall3) == ucode_str
+    assert latex(ip_tall3) == \
+        r'\left\langle \frac{x}{2} \right. {\left|x\right\rangle }'
+    sT(ip_tall3,
+       "InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Symbol('x')))")
+
+
+def test_operator():
+    a = Operator('A')
+    b = Operator('B', Symbol('t'), S.Half)
+    inv = a.inv()
+    f = Function('f')
+    x = symbols('x')
+    d = DifferentialOperator(Derivative(f(x), x), f(x))
+    op = OuterProduct(Ket(), Bra())
+    assert str(a) == 'A'
+    assert pretty(a) == 'A'
+    assert upretty(a) == 'A'
+    assert latex(a) == 'A'
+    sT(a, "Operator(Symbol('A'))")
+    assert str(inv) == 'A**(-1)'
+    ascii_str = \
+"""\
+ -1\n\
+A  \
+"""
+    ucode_str = \
+"""\
+ -1\n\
+A  \
+"""
+    assert pretty(inv) == ascii_str
+    assert upretty(inv) == ucode_str
+    assert latex(inv) == r'A^{-1}'
+    sT(inv, "Pow(Operator(Symbol('A')), Integer(-1))")
+    assert str(d) == 'DifferentialOperator(Derivative(f(x), x),f(x))'
+    ascii_str = \
+"""\
+                    /d            \\\n\
+DifferentialOperator|--(f(x)),f(x)|\n\
+                    \\dx           /\
+"""
+    ucode_str = \
+"""\
+                    ⎛d            ⎞\n\
+DifferentialOperator⎜──(f(x)),f(x)⎟\n\
+                    ⎝dx           ⎠\
+"""
+    assert pretty(d) == ascii_str
+    assert upretty(d) == ucode_str
+    assert latex(d) == \
+        r'DifferentialOperator\left(\frac{d}{d x} f{\left(x \right)},f{\left(x \right)}\right)'
+    sT(d, "DifferentialOperator(Derivative(Function('f')(Symbol('x')), Tuple(Symbol('x'), Integer(1))),Function('f')(Symbol('x')))")
+    assert str(b) == 'Operator(B,t,1/2)'
+    assert pretty(b) == 'Operator(B,t,1/2)'
+    assert upretty(b) == 'Operator(B,t,1/2)'
+    assert latex(b) == r'Operator\left(B,t,\frac{1}{2}\right)'
+    sT(b, "Operator(Symbol('B'),Symbol('t'),Rational(1, 2))")
+    assert str(op) == '|psi><psi|'
+    assert pretty(op) == '|psi><psi|'
+    assert upretty(op) == '❘ψ⟩⟨ψ❘'
+    assert latex(op) == r'{\left|\psi\right\rangle }{\left\langle \psi\right|}'
+    sT(op, "OuterProduct(Ket(Symbol('psi')),Bra(Symbol('psi')))")
+
+
+def test_qexpr():
+    q = QExpr('q')
+    assert str(q) == 'q'
+    assert pretty(q) == 'q'
+    assert upretty(q) == 'q'
+    assert latex(q) == r'q'
+    sT(q, "QExpr(Symbol('q'))")
+
+
+def test_qubit():
+    q1 = Qubit('0101')
+    q2 = IntQubit(8)
+    assert str(q1) == '|0101>'
+    assert pretty(q1) == '|0101>'
+    assert upretty(q1) == '❘0101⟩'
+    assert latex(q1) == r'{\left|0101\right\rangle }'
+    sT(q1, "Qubit(Integer(0),Integer(1),Integer(0),Integer(1))")
+    assert str(q2) == '|8>'
+    assert pretty(q2) == '|8>'
+    assert upretty(q2) == '❘8⟩'
+    assert latex(q2) == r'{\left|8\right\rangle }'
+    sT(q2, "IntQubit(8)")
+
+
+def test_spin():
+    lz = JzOp('L')
+    ket = JzKet(1, 0)
+    bra = JzBra(1, 0)
+    cket = JzKetCoupled(1, 0, (1, 2))
+    cbra = JzBraCoupled(1, 0, (1, 2))
+    cket_big = JzKetCoupled(1, 0, (1, 2, 3))
+    cbra_big = JzBraCoupled(1, 0, (1, 2, 3))
+    rot = Rotation(1, 2, 3)
+    bigd = WignerD(1, 2, 3, 4, 5, 6)
+    smalld = WignerD(1, 2, 3, 0, 4, 0)
+    assert str(lz) == 'Lz'
+    ascii_str = \
+"""\
+L \n\
+ z\
+"""
+    ucode_str = \
+"""\
+L \n\
+ z\
+"""
+    assert pretty(lz) == ascii_str
+    assert upretty(lz) == ucode_str
+    assert latex(lz) == 'L_z'
+    sT(lz, "JzOp(Symbol('L'))")
+    assert str(J2) == 'J2'
+    ascii_str = \
+"""\
+ 2\n\
+J \
+"""
+    ucode_str = \
+"""\
+ 2\n\
+J \
+"""
+    assert pretty(J2) == ascii_str
+    assert upretty(J2) == ucode_str
+    assert latex(J2) == r'J^2'
+    sT(J2, "J2Op(Symbol('J'))")
+    assert str(Jz) == 'Jz'
+    ascii_str = \
+"""\
+J \n\
+ z\
+"""
+    ucode_str = \
+"""\
+J \n\
+ z\
+"""
+    assert pretty(Jz) == ascii_str
+    assert upretty(Jz) == ucode_str
+    assert latex(Jz) == 'J_z'
+    sT(Jz, "JzOp(Symbol('J'))")
+    assert str(ket) == '|1,0>'
+    assert pretty(ket) == '|1,0>'
+    assert upretty(ket) == '❘1,0⟩'
+    assert latex(ket) == r'{\left|1,0\right\rangle }'
+    sT(ket, "JzKet(Integer(1),Integer(0))")
+    assert str(bra) == '<1,0|'
+    assert pretty(bra) == '<1,0|'
+    assert upretty(bra) == '⟨1,0❘'
+    assert latex(bra) == r'{\left\langle 1,0\right|}'
+    sT(bra, "JzBra(Integer(1),Integer(0))")
+    assert str(cket) == '|1,0,j1=1,j2=2>'
+    assert pretty(cket) == '|1,0,j1=1,j2=2>'
+    assert upretty(cket) == '❘1,0,j₁=1,j₂=2⟩'
+    assert latex(cket) == r'{\left|1,0,j_{1}=1,j_{2}=2\right\rangle }'
+    sT(cket, "JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))")
+    assert str(cbra) == '<1,0,j1=1,j2=2|'
+    assert pretty(cbra) == '<1,0,j1=1,j2=2|'
+    assert upretty(cbra) == '⟨1,0,j₁=1,j₂=2❘'
+    assert latex(cbra) == r'{\left\langle 1,0,j_{1}=1,j_{2}=2\right|}'
+    sT(cbra, "JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))")
+    assert str(cket_big) == '|1,0,j1=1,j2=2,j3=3,j(1,2)=3>'
+    # TODO: Fix non-unicode pretty printing
+    # i.e. j1,2 -> j(1,2)
+    assert pretty(cket_big) == '|1,0,j1=1,j2=2,j3=3,j1,2=3>'
+    assert upretty(cket_big) == '❘1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3⟩'
+    assert latex(cket_big) == \
+        r'{\left|1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right\rangle }'
+    sT(cket_big, "JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))")
+    assert str(cbra_big) == '<1,0,j1=1,j2=2,j3=3,j(1,2)=3|'
+    assert pretty(cbra_big) == '<1,0,j1=1,j2=2,j3=3,j1,2=3|'
+    assert upretty(cbra_big) == '⟨1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3❘'
+    assert latex(cbra_big) == \
+        r'{\left\langle 1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right|}'
+    sT(cbra_big, "JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))")
+    assert str(rot) == 'R(1,2,3)'
+    assert pretty(rot) == 'R (1,2,3)'
+    assert upretty(rot) == 'ℛ (1,2,3)'
+    assert latex(rot) == r'\mathcal{R}\left(1,2,3\right)'
+    sT(rot, "Rotation(Integer(1),Integer(2),Integer(3))")
+    assert str(bigd) == 'WignerD(1, 2, 3, 4, 5, 6)'
+    ascii_str = \
+"""\
+ 1         \n\
+D   (4,5,6)\n\
+ 2,3       \
+"""
+    ucode_str = \
+"""\
+ 1         \n\
+D   (4,5,6)\n\
+ 2,3       \
+"""
+    assert pretty(bigd) == ascii_str
+    assert upretty(bigd) == ucode_str
+    assert latex(bigd) == r'D^{1}_{2,3}\left(4,5,6\right)'
+    sT(bigd, "WignerD(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))")
+    assert str(smalld) == 'WignerD(1, 2, 3, 0, 4, 0)'
+    ascii_str = \
+"""\
+ 1     \n\
+d   (4)\n\
+ 2,3   \
+"""
+    ucode_str = \
+"""\
+ 1     \n\
+d   (4)\n\
+ 2,3   \
+"""
+    assert pretty(smalld) == ascii_str
+    assert upretty(smalld) == ucode_str
+    assert latex(smalld) == r'd^{1}_{2,3}\left(4\right)'
+    sT(smalld, "WignerD(Integer(1), Integer(2), Integer(3), Integer(0), Integer(4), Integer(0))")
+
+
+def test_state():
+    x = symbols('x')
+    bra = Bra()
+    ket = Ket()
+    bra_tall = Bra(x/2)
+    ket_tall = Ket(x/2)
+    tbra = TimeDepBra()
+    tket = TimeDepKet()
+    assert str(bra) == '<psi|'
+    assert pretty(bra) == '<psi|'
+    assert upretty(bra) == '⟨ψ❘'
+    assert latex(bra) == r'{\left\langle \psi\right|}'
+    sT(bra, "Bra(Symbol('psi'))")
+    assert str(ket) == '|psi>'
+    assert pretty(ket) == '|psi>'
+    assert upretty(ket) == '❘ψ⟩'
+    assert latex(ket) == r'{\left|\psi\right\rangle }'
+    sT(ket, "Ket(Symbol('psi'))")
+    assert str(bra_tall) == '<x/2|'
+    ascii_str = \
+"""\
+ / |\n\
+/ x|\n\
+\\ -|\n\
+ \\2|\
+"""
+    ucode_str = \
+"""\
+ ╱ │\n\
+╱ x│\n\
+╲ ─│\n\
+ ╲2│\
+"""
+    assert pretty(bra_tall) == ascii_str
+    assert upretty(bra_tall) == ucode_str
+    assert latex(bra_tall) == r'{\left\langle \frac{x}{2}\right|}'
+    sT(bra_tall, "Bra(Mul(Rational(1, 2), Symbol('x')))")
+    assert str(ket_tall) == '|x/2>'
+    ascii_str = \
+"""\
+| \\ \n\
+|x \\\n\
+|- /\n\
+|2/ \
+"""
+    ucode_str = \
+"""\
+│ ╲ \n\
+│x ╲\n\
+│─ ╱\n\
+│2╱ \
+"""
+    assert pretty(ket_tall) == ascii_str
+    assert upretty(ket_tall) == ucode_str
+    assert latex(ket_tall) == r'{\left|\frac{x}{2}\right\rangle }'
+    sT(ket_tall, "Ket(Mul(Rational(1, 2), Symbol('x')))")
+    assert str(tbra) == '<psi;t|'
+    assert pretty(tbra) == '<psi;t|'
+    assert upretty(tbra) == '⟨ψ;t❘'
+    assert latex(tbra) == r'{\left\langle \psi;t\right|}'
+    sT(tbra, "TimeDepBra(Symbol('psi'),Symbol('t'))")
+    assert str(tket) == '|psi;t>'
+    assert pretty(tket) == '|psi;t>'
+    assert upretty(tket) == '❘ψ;t⟩'
+    assert latex(tket) == r'{\left|\psi;t\right\rangle }'
+    sT(tket, "TimeDepKet(Symbol('psi'),Symbol('t'))")
+
+
+def test_tensorproduct():
+    tp = TensorProduct(JzKet(1, 1), JzKet(1, 0))
+    assert str(tp) == '|1,1>x|1,0>'
+    assert pretty(tp) == '|1,1>x |1,0>'
+    assert upretty(tp) == '❘1,1⟩⨂ ❘1,0⟩'
+    assert latex(tp) == \
+        r'{{\left|1,1\right\rangle }}\otimes {{\left|1,0\right\rangle }}'
+    sT(tp, "TensorProduct(JzKet(Integer(1),Integer(1)), JzKet(Integer(1),Integer(0)))")
+
+
+def test_big_expr():
+    f = Function('f')
+    x = symbols('x')
+    e1 = Dagger(AntiCommutator(Operator('A') + Operator('B'), Pow(DifferentialOperator(Derivative(f(x), x), f(x)), 3))*TensorProduct(Jz**2, Operator('A') + Operator('B')))*(JzBra(1, 0) + JzBra(1, 1))*(JzKet(0, 0) + JzKet(1, -1))
+    e2 = Commutator(Jz**2, Operator('A') + Operator('B'))*AntiCommutator(Dagger(Operator('C')*Operator('D')), Operator('E').inv()**2)*Dagger(Commutator(Jz, J2))
+    e3 = Wigner3j(1, 2, 3, 4, 5, 6)*TensorProduct(Commutator(Operator('A') + Dagger(Operator('B')), Operator('C') + Operator('D')), Jz - J2)*Dagger(OuterProduct(Dagger(JzBra(1, 1)), JzBra(1, 0)))*TensorProduct(JzKetCoupled(1, 1, (1, 1)) + JzKetCoupled(1, 0, (1, 1)), JzKetCoupled(1, -1, (1, 1)))
+    e4 = (ComplexSpace(1)*ComplexSpace(2) + FockSpace()**2)*(L2(Interval(
+        0, oo)) + HilbertSpace())
+    assert str(e1) == '(Jz**2)x(Dagger(A) + Dagger(B))*{Dagger(DifferentialOperator(Derivative(f(x), x),f(x)))**3,Dagger(A) + Dagger(B)}*(<1,0| + <1,1|)*(|0,0> + |1,-1>)'
+    ascii_str = \
+"""\
+                 /                                      3        \\                                 \n\
+                 |/                                   +\\         |                                 \n\
+    2  / +    +\\ <|                    /d            \\ |   +    +>                                 \n\
+/J \\ x \\A  + B /*||DifferentialOperator|--(f(x)),f(x)| | ,A  + B |*(<1,0| + <1,1|)*(|0,0> + |1,-1>)\n\
+\\ z/             \\\\                    \\dx           / /         /                                 \
+"""
+    ucode_str = \
+"""\
+                 ⎧                                      3        ⎫                                 \n\
+                 ⎪⎛                                   †⎞         ⎪                                 \n\
+    2  ⎛ †    †⎞ ⎨⎜                    ⎛d            ⎞ ⎟   †    †⎬                                 \n\
+⎛J ⎞ ⨂ ⎝A  + B ⎠⋅⎪⎜DifferentialOperator⎜──(f(x)),f(x)⎟ ⎟ ,A  + B ⎪⋅(⟨1,0❘ + ⟨1,1❘)⋅(❘0,0⟩ + ❘1,-1⟩)\n\
+⎝ z⎠             ⎩⎝                    ⎝dx           ⎠ ⎠         ⎭                                 \
+"""
+    assert pretty(e1) == ascii_str
+    assert upretty(e1) == ucode_str
+    assert latex(e1) == \
+        r'{J_z^{2}}\otimes \left({A^{\dagger} + B^{\dagger}}\right) \left\{\left(DifferentialOperator\left(\frac{d}{d x} f{\left(x \right)},f{\left(x \right)}\right)^{\dagger}\right)^{3},A^{\dagger} + B^{\dagger}\right\} \left({\left\langle 1,0\right|} + {\left\langle 1,1\right|}\right) \left({\left|0,0\right\rangle } + {\left|1,-1\right\rangle }\right)'
+    sT(e1, "Mul(TensorProduct(Pow(JzOp(Symbol('J')), Integer(2)), Add(Dagger(Operator(Symbol('A'))), Dagger(Operator(Symbol('B'))))), AntiCommutator(Pow(Dagger(DifferentialOperator(Derivative(Function('f')(Symbol('x')), Tuple(Symbol('x'), Integer(1))),Function('f')(Symbol('x')))), Integer(3)),Add(Dagger(Operator(Symbol('A'))), Dagger(Operator(Symbol('B'))))), Add(JzBra(Integer(1),Integer(0)), JzBra(Integer(1),Integer(1))), Add(JzKet(Integer(0),Integer(0)), JzKet(Integer(1),Integer(-1))))")
+    assert str(e2) == '[Jz**2,A + B]*{E**(-2),Dagger(D)*Dagger(C)}*[J2,Jz]'
+    ascii_str = \
+"""\
+[    2      ] / -2  +  +\\ [ 2   ]\n\
+[/J \\ ,A + B]*<E  ,D *C >*[J ,J ]\n\
+[\\ z/       ] \\         / [    z]\
+"""
+    ucode_str = \
+"""\
+⎡    2      ⎤ ⎧ -2  †  †⎫ ⎡ 2   ⎤\n\
+⎢⎛J ⎞ ,A + B⎥⋅⎨E  ,D ⋅C ⎬⋅⎢J ,J ⎥\n\
+⎣⎝ z⎠       ⎦ ⎩         ⎭ ⎣    z⎦\
+"""
+    assert pretty(e2) == ascii_str
+    assert upretty(e2) == ucode_str
+    assert latex(e2) == \
+        r'\left[J_z^{2},A + B\right] \left\{E^{-2},D^{\dagger} C^{\dagger}\right\} \left[J^2,J_z\right]'
+    sT(e2, "Mul(Commutator(Pow(JzOp(Symbol('J')), Integer(2)),Add(Operator(Symbol('A')), Operator(Symbol('B')))), AntiCommutator(Pow(Operator(Symbol('E')), Integer(-2)),Mul(Dagger(Operator(Symbol('D'))), Dagger(Operator(Symbol('C'))))), Commutator(J2Op(Symbol('J')),JzOp(Symbol('J'))))")
+    assert str(e3) == \
+        "Wigner3j(1, 2, 3, 4, 5, 6)*[Dagger(B) + A,C + D]x(-J2 + Jz)*|1,0><1,1|*(|1,0,j1=1,j2=1> + |1,1,j1=1,j2=1>)x|1,-1,j1=1,j2=1>"
+    ascii_str = \
+"""\
+          [ +          ]  /   2     \\                                                                 \n\
+/1  3  5\\*[B  + A,C + D]x |- J  + J |*|1,0><1,1|*(|1,0,j1=1,j2=1> + |1,1,j1=1,j2=1>)x |1,-1,j1=1,j2=1>\n\
+|       |                 \\        z/                                                                 \n\
+\\2  4  6/                                                                                             \
+"""
+    ucode_str = \
+"""\
+          ⎡ †          ⎤  ⎛   2     ⎞                                                                 \n\
+⎛1  3  5⎞⋅⎣B  + A,C + D⎦⨂ ⎜- J  + J ⎟⋅❘1,0⟩⟨1,1❘⋅(❘1,0,j₁=1,j₂=1⟩ + ❘1,1,j₁=1,j₂=1⟩)⨂ ❘1,-1,j₁=1,j₂=1⟩\n\
+⎜       ⎟                 ⎝        z⎠                                                                 \n\
+⎝2  4  6⎠                                                                                             \
+"""
+    assert pretty(e3) == ascii_str
+    assert upretty(e3) == ucode_str
+    assert latex(e3) == \
+        r'\left(\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 4 & 6 \end{array}\right) {\left[B^{\dagger} + A,C + D\right]}\otimes \left({- J^2 + J_z}\right) {\left|1,0\right\rangle }{\left\langle 1,1\right|} \left({{\left|1,0,j_{1}=1,j_{2}=1\right\rangle } + {\left|1,1,j_{1}=1,j_{2}=1\right\rangle }}\right)\otimes {{\left|1,-1,j_{1}=1,j_{2}=1\right\rangle }}'
+    sT(e3, "Mul(Wigner3j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6)), TensorProduct(Commutator(Add(Dagger(Operator(Symbol('B'))), Operator(Symbol('A'))),Add(Operator(Symbol('C')), Operator(Symbol('D')))), Add(Mul(Integer(-1), J2Op(Symbol('J'))), JzOp(Symbol('J')))), OuterProduct(JzKet(Integer(1),Integer(0)),JzBra(Integer(1),Integer(1))), TensorProduct(Add(JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))), JzKetCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))), JzKetCoupled(Integer(1),Integer(-1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))))")
+    assert str(e4) == '(C(1)*C(2)+F**2)*(L2(Interval(0, oo))+H)'
+    ascii_str = \
+"""\
+// 1    2\\    x2\\   / 2    \\\n\
+\\\\C  x C / + F  / x \\L  + H/\
+"""
+    ucode_str = \
+"""\
+⎛⎛ 1    2⎞    ⨂2⎞   ⎛ 2    ⎞\n\
+⎝⎝C  ⨂ C ⎠ ⊕ F  ⎠ ⨂ ⎝L  ⊕ H⎠\
+"""
+    assert pretty(e4) == ascii_str
+    assert upretty(e4) == ucode_str
+    assert latex(e4) == \
+        r'\left(\left(\mathcal{C}^{1}\otimes \mathcal{C}^{2}\right)\oplus {\mathcal{F}}^{\otimes 2}\right)\otimes \left({\mathcal{L}^2}\left( \left[0, \infty\right) \right)\oplus \mathcal{H}\right)'
+    sT(e4, "TensorProductHilbertSpace((DirectSumHilbertSpace(TensorProductHilbertSpace(ComplexSpace(Integer(1)),ComplexSpace(Integer(2))),TensorPowerHilbertSpace(FockSpace(),Integer(2)))),(DirectSumHilbertSpace(L2(Interval(Integer(0), oo, false, true)),HilbertSpace())))")
+
+
+def _test_sho1d():
+    ad = RaisingOp('a')
+    assert pretty(ad) == ' \N{DAGGER}\na '
+    assert latex(ad) == 'a^{\\dagger}'

rl/Lib/site-packages/sympy/physics/quantum/tests/test_qapply.py

@@ -0,0 +1,150 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.constants import hbar
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.gate import H, XGate, IdentityGate
+from sympy.physics.quantum.operator import Operator, IdentityOperator
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.spin import Jx, Jy, Jz, Jplus, Jminus, J2, JzKet
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.state import Ket
+from sympy.physics.quantum.density import Density
+from sympy.physics.quantum.qubit import Qubit, QubitBra
+from sympy.physics.quantum.boson import BosonOp, BosonFockKet, BosonFockBra
+
+
+j, jp, m, mp = symbols("j j' m m'")
+
+z = JzKet(1, 0)
+po = JzKet(1, 1)
+mo = JzKet(1, -1)
+
+A = Operator('A')
+
+
+class Foo(Operator):
+    def _apply_operator_JzKet(self, ket, **options):
+        return ket
+
+
+def test_basic():
+    assert qapply(Jz*po) == hbar*po
+    assert qapply(Jx*z) == hbar*po/sqrt(2) + hbar*mo/sqrt(2)
+    assert qapply((Jplus + Jminus)*z/sqrt(2)) == hbar*po + hbar*mo
+    assert qapply(Jz*(po + mo)) == hbar*po - hbar*mo
+    assert qapply(Jz*po + Jz*mo) == hbar*po - hbar*mo
+    assert qapply(Jminus*Jminus*po) == 2*hbar**2*mo
+    assert qapply(Jplus**2*mo) == 2*hbar**2*po
+    assert qapply(Jplus**2*Jminus**2*po) == 4*hbar**4*po
+
+
+def test_extra():
+    extra = z.dual*A*z
+    assert qapply(Jz*po*extra) == hbar*po*extra
+    assert qapply(Jx*z*extra) == (hbar*po/sqrt(2) + hbar*mo/sqrt(2))*extra
+    assert qapply(
+        (Jplus + Jminus)*z/sqrt(2)*extra) == hbar*po*extra + hbar*mo*extra
+    assert qapply(Jz*(po + mo)*extra) == hbar*po*extra - hbar*mo*extra
+    assert qapply(Jz*po*extra + Jz*mo*extra) == hbar*po*extra - hbar*mo*extra
+    assert qapply(Jminus*Jminus*po*extra) == 2*hbar**2*mo*extra
+    assert qapply(Jplus**2*mo*extra) == 2*hbar**2*po*extra
+    assert qapply(Jplus**2*Jminus**2*po*extra) == 4*hbar**4*po*extra
+
+
+def test_innerproduct():
+    assert qapply(po.dual*Jz*po, ip_doit=False) == hbar*(po.dual*po)
+    assert qapply(po.dual*Jz*po) == hbar
+
+
+def test_zero():
+    assert qapply(0) == 0
+    assert qapply(Integer(0)) == 0
+
+
+def test_commutator():
+    assert qapply(Commutator(Jx, Jy)*Jz*po) == I*hbar**3*po
+    assert qapply(Commutator(J2, Jz)*Jz*po) == 0
+    assert qapply(Commutator(Jz, Foo('F'))*po) == 0
+    assert qapply(Commutator(Foo('F'), Jz)*po) == 0
+
+
+def test_anticommutator():
+    assert qapply(AntiCommutator(Jz, Foo('F'))*po) == 2*hbar*po
+    assert qapply(AntiCommutator(Foo('F'), Jz)*po) == 2*hbar*po
+
+
+def test_outerproduct():
+    e = Jz*(mo*po.dual)*Jz*po
+    assert qapply(e) == -hbar**2*mo
+    assert qapply(e, ip_doit=False) == -hbar**2*(po.dual*po)*mo
+    assert qapply(e).doit() == -hbar**2*mo
+
+
+def test_tensorproduct():
+    a = BosonOp("a")
+    b = BosonOp("b")
+    ket1 = TensorProduct(BosonFockKet(1), BosonFockKet(2))
+    ket2 = TensorProduct(BosonFockKet(0), BosonFockKet(0))
+    ket3 = TensorProduct(BosonFockKet(0), BosonFockKet(2))
+    bra1 = TensorProduct(BosonFockBra(0), BosonFockBra(0))
+    bra2 = TensorProduct(BosonFockBra(1), BosonFockBra(2))
+    assert qapply(TensorProduct(a, b ** 2) * ket1) == sqrt(2) * ket2
+    assert qapply(TensorProduct(a, Dagger(b) * b) * ket1) == 2 * ket3
+    assert qapply(bra1 * TensorProduct(a, b * b),
+                  dagger=True) == sqrt(2) * bra2
+    assert qapply(bra2 * ket1).doit() == TensorProduct(1, 1)
+    assert qapply(TensorProduct(a, b * b) * ket1) == sqrt(2) * ket2
+    assert qapply(Dagger(TensorProduct(a, b * b) * ket1),
+                  dagger=True) == sqrt(2) * Dagger(ket2)
+
+
+def test_dagger():
+    lhs = Dagger(Qubit(0))*Dagger(H(0))
+    rhs = Dagger(Qubit(1))/sqrt(2) + Dagger(Qubit(0))/sqrt(2)
+    assert qapply(lhs, dagger=True) == rhs
+
+
+def test_issue_6073():
+    x, y = symbols('x y', commutative=False)
+    A = Ket(x, y)
+    B = Operator('B')
+    assert qapply(A) == A
+    assert qapply(A.dual*B) == A.dual*B
+
+
+def test_density():
+    d = Density([Jz*mo, 0.5], [Jz*po, 0.5])
+    assert qapply(d) == Density([-hbar*mo, 0.5], [hbar*po, 0.5])
+
+
+def test_issue3044():
+    expr1 = TensorProduct(Jz*JzKet(S(2),S.NegativeOne)/sqrt(2), Jz*JzKet(S.Half,S.Half))
+    result = Mul(S.NegativeOne, Rational(1, 4), 2**S.Half, hbar**2)
+    result *= TensorProduct(JzKet(2,-1), JzKet(S.Half,S.Half))
+    assert qapply(expr1) == result
+
+
+# Issue 24158: Tests whether qapply incorrectly evaluates some ket*op as op*ket
+def test_issue24158_ket_times_op():
+    P = BosonFockKet(0) * BosonOp("a") # undefined term
+    # Does lhs._apply_operator_BosonOp(rhs) still evaluate ket*op as op*ket?
+    assert qapply(P) == P   # qapply(P) -> BosonOp("a")*BosonFockKet(0) = 0 before fix
+    P = Qubit(1) * XGate(0) # undefined term
+    # Does rhs._apply_operator_Qubit(lhs) still evaluate ket*op as op*ket?
+    assert qapply(P) == P   # qapply(P) -> Qubit(0) before fix
+    P1 = Mul(QubitBra(0), Mul(QubitBra(0), Qubit(0)), XGate(0)) # legal expr <0| * (<1|*|1>) * X
+    assert qapply(P1) == QubitBra(0) * XGate(0)     # qapply(P1) -> 0 before fix
+    P1 = qapply(P1, dagger = True)  # unsatisfactorily -> <0|*X(0), expect <1| since dagger=True
+    assert qapply(P1, dagger = True) == QubitBra(1) # qapply(P1, dagger=True) -> 0 before fix
+    P2 = QubitBra(0) * QubitBra(0) * Qubit(0) * XGate(0) # 'forgot' to set brackets
+    P2 = qapply(P2, dagger = True) # unsatisfactorily -> <0|*X(0), expect <1| since dagger=True
+    assert qapply(P2, dagger = True) == QubitBra(1) # qapply(P1) -> 0 before fix
+    # Pull Request 24237: IdentityOperator from the right without dagger=True option
+    assert qapply(QubitBra(1)*IdentityOperator()) == QubitBra(1)
+    assert qapply(IdentityGate(0)*(Qubit(0) + Qubit(1))) == Qubit(0) + Qubit(1)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_qasm.py

@@ -0,0 +1,89 @@
+from sympy.physics.quantum.qasm import Qasm, flip_index, trim,\
+     get_index, nonblank, fullsplit, fixcommand, stripquotes, read_qasm
+from sympy.physics.quantum.gate import X, Z, H, S, T
+from sympy.physics.quantum.gate import CNOT, SWAP, CPHASE, CGate, CGateS
+from sympy.physics.quantum.circuitplot import Mz
+
+def test_qasm_readqasm():
+    qasm_lines = """\
+    qubit q_0
+    qubit q_1
+    h q_0
+    cnot q_0,q_1
+    """
+    q = read_qasm(qasm_lines)
+    assert q.get_circuit() == CNOT(1,0)*H(1)
+
+def test_qasm_ex1():
+    q = Qasm('qubit q0', 'qubit q1', 'h q0', 'cnot q0,q1')
+    assert q.get_circuit() == CNOT(1,0)*H(1)
+
+def test_qasm_ex1_methodcalls():
+    q = Qasm()
+    q.qubit('q_0')
+    q.qubit('q_1')
+    q.h('q_0')
+    q.cnot('q_0', 'q_1')
+    assert q.get_circuit() == CNOT(1,0)*H(1)
+
+def test_qasm_swap():
+    q = Qasm('qubit q0', 'qubit q1', 'cnot q0,q1', 'cnot q1,q0', 'cnot q0,q1')
+    assert q.get_circuit() == CNOT(1,0)*CNOT(0,1)*CNOT(1,0)
+
+
+def test_qasm_ex2():
+    q = Qasm('qubit q_0', 'qubit q_1', 'qubit q_2', 'h  q_1',
+             'cnot q_1,q_2', 'cnot q_0,q_1', 'h q_0',
+             'measure q_1', 'measure q_0',
+             'c-x q_1,q_2', 'c-z q_0,q_2')
+    assert q.get_circuit() == CGate(2,Z(0))*CGate(1,X(0))*Mz(2)*Mz(1)*H(2)*CNOT(2,1)*CNOT(1,0)*H(1)
+
+def test_qasm_1q():
+    for symbol, gate in [('x', X), ('z', Z), ('h', H), ('s', S), ('t', T), ('measure', Mz)]:
+        q = Qasm('qubit q_0', '%s q_0' % symbol)
+        assert q.get_circuit() == gate(0)
+
+def test_qasm_2q():
+    for symbol, gate in [('cnot', CNOT), ('swap', SWAP), ('cphase', CPHASE)]:
+        q = Qasm('qubit q_0', 'qubit q_1', '%s q_0,q_1' % symbol)
+        assert q.get_circuit() == gate(1,0)
+
+def test_qasm_3q():
+    q = Qasm('qubit q0', 'qubit q1', 'qubit q2', 'toffoli q2,q1,q0')
+    assert q.get_circuit() == CGateS((0,1),X(2))
+
+def test_qasm_flip_index():
+    assert flip_index(0, 2) == 1
+    assert flip_index(1, 2) == 0
+
+def test_qasm_trim():
+    assert trim('nothing happens here') == 'nothing happens here'
+    assert trim("Something #happens here") == "Something "
+
+def test_qasm_get_index():
+    assert get_index('q0', ['q0', 'q1']) == 1
+    assert get_index('q1', ['q0', 'q1']) == 0
+
+def test_qasm_nonblank():
+    assert list(nonblank('abcd')) == list('abcd')
+    assert list(nonblank('abc ')) == list('abc')
+
+def test_qasm_fullsplit():
+    assert fullsplit('g q0,q1,q2,  q3') == ('g', ['q0', 'q1', 'q2', 'q3'])
+
+def test_qasm_fixcommand():
+    assert fixcommand('foo') == 'foo'
+    assert fixcommand('def') == 'qdef'
+
+def test_qasm_stripquotes():
+    assert stripquotes("'S'") == 'S'
+    assert stripquotes('"S"') == 'S'
+    assert stripquotes('S') == 'S'
+
+def test_qasm_qdef():
+    # weaker test condition (str) since we don't have access to the actual class
+    q = Qasm("def Q,0,Q",'qubit q0','Q q0')
+    assert str(q.get_circuit()) == 'Q(0)'
+
+    q = Qasm("def CQ,1,Q", 'qubit q0', 'qubit q1', 'CQ q0,q1')
+    assert str(q.get_circuit()) == 'C((1),Q(0))'

rl/Lib/site-packages/sympy/physics/quantum/tests/test_qexpr.py

@@ -0,0 +1,52 @@
+from sympy.core.numbers import Integer
+from sympy.core.symbol import Symbol
+from sympy.physics.quantum.qexpr import QExpr, _qsympify_sequence
+from sympy.physics.quantum.hilbert import HilbertSpace
+from sympy.core.containers import Tuple
+
+x = Symbol('x')
+y = Symbol('y')
+
+
+def test_qexpr_new():
+    q = QExpr(0)
+    assert q.label == (0,)
+    assert q.hilbert_space == HilbertSpace()
+    assert q.is_commutative is False
+
+    q = QExpr(0, 1)
+    assert q.label == (Integer(0), Integer(1))
+
+    q = QExpr._new_rawargs(HilbertSpace(), Integer(0), Integer(1))
+    assert q.label == (Integer(0), Integer(1))
+    assert q.hilbert_space == HilbertSpace()
+
+
+def test_qexpr_commutative():
+    q1 = QExpr(x)
+    q2 = QExpr(y)
+    assert q1.is_commutative is False
+    assert q2.is_commutative is False
+    assert q1*q2 != q2*q1
+
+    q = QExpr._new_rawargs(Integer(0), Integer(1), HilbertSpace())
+    assert q.is_commutative is False
+
+def test_qexpr_commutative_free_symbols():
+    q1 = QExpr(x)
+    assert q1.free_symbols.pop().is_commutative is False
+
+    q2 = QExpr('q2')
+    assert q2.free_symbols.pop().is_commutative is False
+
+def test_qexpr_subs():
+    q1 = QExpr(x, y)
+    assert q1.subs(x, y) == QExpr(y, y)
+    assert q1.subs({x: 1, y: 2}) == QExpr(1, 2)
+
+
+def test_qsympify():
+    assert _qsympify_sequence([[1, 2], [1, 3]]) == (Tuple(1, 2), Tuple(1, 3))
+    assert _qsympify_sequence(([1, 2, [3, 4, [2, ]], 1], 3)) == \
+        (Tuple(1, 2, Tuple(3, 4, Tuple(2,)), 1), 3)
+    assert _qsympify_sequence((1,)) == (1,)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_qft.py

@@ -0,0 +1,52 @@
+from sympy.core.numbers import (I, pi)
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import Matrix
+
+from sympy.physics.quantum.qft import QFT, IQFT, RkGate
+from sympy.physics.quantum.gate import (ZGate, SwapGate, HadamardGate, CGate,
+                                        PhaseGate, TGate)
+from sympy.physics.quantum.qubit import Qubit
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.represent import represent
+
+from sympy.functions.elementary.complexes import sign
+
+
+def test_RkGate():
+    x = Symbol('x')
+    assert RkGate(1, x).k == x
+    assert RkGate(1, x).targets == (1,)
+    assert RkGate(1, 1) == ZGate(1)
+    assert RkGate(2, 2) == PhaseGate(2)
+    assert RkGate(3, 3) == TGate(3)
+
+    assert represent(
+        RkGate(0, x), nqubits=1) == Matrix([[1, 0], [0, exp(sign(x)*2*pi*I/(2**abs(x)))]])
+
+
+def test_quantum_fourier():
+    assert QFT(0, 3).decompose() == \
+        SwapGate(0, 2)*HadamardGate(0)*CGate((0,), PhaseGate(1)) * \
+        HadamardGate(1)*CGate((0,), TGate(2))*CGate((1,), PhaseGate(2)) * \
+        HadamardGate(2)
+
+    assert IQFT(0, 3).decompose() == \
+        HadamardGate(2)*CGate((1,), RkGate(2, -2))*CGate((0,), RkGate(2, -3)) * \
+        HadamardGate(1)*CGate((0,), RkGate(1, -2))*HadamardGate(0)*SwapGate(0, 2)
+
+    assert represent(QFT(0, 3), nqubits=3) == \
+        Matrix([[exp(2*pi*I/8)**(i*j % 8)/sqrt(8) for i in range(8)] for j in range(8)])
+
+    assert QFT(0, 4).decompose()  # non-trivial decomposition
+    assert qapply(QFT(0, 3).decompose()*Qubit(0, 0, 0)).expand() == qapply(
+        HadamardGate(0)*HadamardGate(1)*HadamardGate(2)*Qubit(0, 0, 0)
+    ).expand()
+
+
+def test_qft_represent():
+    c = QFT(0, 3)
+    a = represent(c, nqubits=3)
+    b = represent(c.decompose(), nqubits=3)
+    assert a.evalf(n=10) == b.evalf(n=10)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_qubit.py

@@ -0,0 +1,255 @@
+import random
+
+from sympy.core.numbers import (Integer, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import Matrix
+from sympy.physics.quantum.qubit import (measure_all, measure_partial,
+                                         matrix_to_qubit, matrix_to_density,
+                                         qubit_to_matrix, IntQubit,
+                                         IntQubitBra, QubitBra)
+from sympy.physics.quantum.gate import (HadamardGate, CNOT, XGate, YGate,
+                                        ZGate, PhaseGate)
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.shor import Qubit
+from sympy.testing.pytest import raises
+from sympy.physics.quantum.density import Density
+from sympy.physics.quantum.trace import Tr
+
+x, y = symbols('x,y')
+
+epsilon = .000001
+
+
+def test_Qubit():
+    array = [0, 0, 1, 1, 0]
+    qb = Qubit('00110')
+    assert qb.flip(0) == Qubit('00111')
+    assert qb.flip(1) == Qubit('00100')
+    assert qb.flip(4) == Qubit('10110')
+    assert qb.qubit_values == (0, 0, 1, 1, 0)
+    assert qb.dimension == 5
+    for i in range(5):
+        assert qb[i] == array[4 - i]
+    assert len(qb) == 5
+    qb = Qubit('110')
+
+
+def test_QubitBra():
+    qb = Qubit(0)
+    qb_bra = QubitBra(0)
+    assert qb.dual_class() == QubitBra
+    assert qb_bra.dual_class() == Qubit
+
+    qb = Qubit(1, 1, 0)
+    qb_bra = QubitBra(1, 1, 0)
+    assert represent(qb, nqubits=3).H == represent(qb_bra, nqubits=3)
+
+    qb = Qubit(0, 1)
+    qb_bra = QubitBra(1,0)
+    assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(0)
+
+    qb_bra = QubitBra(0, 1)
+    assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(1)
+
+
+def test_IntQubit():
+    # issue 9136
+    iqb = IntQubit(0, nqubits=1)
+    assert qubit_to_matrix(Qubit('0')) == qubit_to_matrix(iqb)
+
+    qb = Qubit('1010')
+    assert qubit_to_matrix(IntQubit(qb)) == qubit_to_matrix(qb)
+
+    iqb = IntQubit(1, nqubits=1)
+    assert qubit_to_matrix(Qubit('1')) == qubit_to_matrix(iqb)
+    assert qubit_to_matrix(IntQubit(1)) == qubit_to_matrix(iqb)
+
+    iqb = IntQubit(7, nqubits=4)
+    assert qubit_to_matrix(Qubit('0111')) == qubit_to_matrix(iqb)
+    assert qubit_to_matrix(IntQubit(7, 4)) == qubit_to_matrix(iqb)
+
+    iqb = IntQubit(8)
+    assert iqb.as_int() == 8
+    assert iqb.qubit_values == (1, 0, 0, 0)
+
+    iqb = IntQubit(7, 4)
+    assert iqb.qubit_values == (0, 1, 1, 1)
+    assert IntQubit(3) == IntQubit(3, 2)
+
+    #test Dual Classes
+    iqb = IntQubit(3)
+    iqb_bra = IntQubitBra(3)
+    assert iqb.dual_class() == IntQubitBra
+    assert iqb_bra.dual_class() == IntQubit
+
+    iqb = IntQubit(5)
+    iqb_bra = IntQubitBra(5)
+    assert iqb._eval_innerproduct_IntQubitBra(iqb_bra) == Integer(1)
+
+    iqb = IntQubit(4)
+    iqb_bra = IntQubitBra(5)
+    assert iqb._eval_innerproduct_IntQubitBra(iqb_bra) == Integer(0)
+    raises(ValueError, lambda: IntQubit(4, 1))
+
+    raises(ValueError, lambda: IntQubit('5'))
+    raises(ValueError, lambda: IntQubit(5, '5'))
+    raises(ValueError, lambda: IntQubit(5, nqubits='5'))
+    raises(TypeError, lambda: IntQubit(5, bad_arg=True))
+
+def test_superposition_of_states():
+    state = 1/sqrt(2)*Qubit('01') + 1/sqrt(2)*Qubit('10')
+    state_gate = CNOT(0, 1)*HadamardGate(0)*state
+    state_expanded = Qubit('01')/2 + Qubit('00')/2 - Qubit('11')/2 + Qubit('10')/2
+    assert qapply(state_gate).expand() == state_expanded
+    assert matrix_to_qubit(represent(state_gate, nqubits=2)) == state_expanded
+
+
+#test apply methods
+def test_apply_represent_equality():
+    gates = [HadamardGate(int(3*random.random())),
+     XGate(int(3*random.random())), ZGate(int(3*random.random())),
+        YGate(int(3*random.random())), ZGate(int(3*random.random())),
+        PhaseGate(int(3*random.random()))]
+
+    circuit = Qubit(int(random.random()*2), int(random.random()*2),
+    int(random.random()*2), int(random.random()*2), int(random.random()*2),
+        int(random.random()*2))
+    for i in range(int(random.random()*6)):
+        circuit = gates[int(random.random()*6)]*circuit
+
+    mat = represent(circuit, nqubits=6)
+    states = qapply(circuit)
+    state_rep = matrix_to_qubit(mat)
+    states = states.expand()
+    state_rep = state_rep.expand()
+    assert state_rep == states
+
+
+def test_matrix_to_qubits():
+    qb = Qubit(0, 0, 0, 0)
+    mat = Matrix([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+    assert matrix_to_qubit(mat) == qb
+    assert qubit_to_matrix(qb) == mat
+
+    state = 2*sqrt(2)*(Qubit(0, 0, 0) + Qubit(0, 0, 1) + Qubit(0, 1, 0) +
+                       Qubit(0, 1, 1) + Qubit(1, 0, 0) + Qubit(1, 0, 1) +
+                       Qubit(1, 1, 0) + Qubit(1, 1, 1))
+    ones = sqrt(2)*2*Matrix([1, 1, 1, 1, 1, 1, 1, 1])
+    assert matrix_to_qubit(ones) == state.expand()
+    assert qubit_to_matrix(state) == ones
+
+
+def test_measure_normalize():
+    a, b = symbols('a b')
+    state = a*Qubit('110') + b*Qubit('111')
+    assert measure_partial(state, (0,), normalize=False) == \
+        [(a*Qubit('110'), a*a.conjugate()), (b*Qubit('111'), b*b.conjugate())]
+    assert measure_all(state, normalize=False) == \
+        [(Qubit('110'), a*a.conjugate()), (Qubit('111'), b*b.conjugate())]
+
+
+def test_measure_partial():
+    #Basic test of collapse of entangled two qubits (Bell States)
+    state = Qubit('01') + Qubit('10')
+    assert measure_partial(state, (0,)) == \
+        [(Qubit('10'), S.Half), (Qubit('01'), S.Half)]
+    assert measure_partial(state, int(0)) == \
+        [(Qubit('10'), S.Half), (Qubit('01'), S.Half)]
+    assert measure_partial(state, (0,)) == \
+        measure_partial(state, (1,))[::-1]
+
+    #Test of more complex collapse and probability calculation
+    state1 = sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111')
+    assert measure_partial(state1, (0,)) == \
+        [(sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111'), 1)]
+    assert measure_partial(state1, (1, 2)) == measure_partial(state1, (3, 4))
+    assert measure_partial(state1, (1, 2, 3)) == \
+        [(Qubit('00001'), Rational(2, 3)), (Qubit('11111'), Rational(1, 3))]
+
+    #test of measuring multiple bits at once
+    state2 = Qubit('1111') + Qubit('1101') + Qubit('1011') + Qubit('1000')
+    assert measure_partial(state2, (0, 1, 3)) == \
+        [(Qubit('1000'), Rational(1, 4)), (Qubit('1101'), Rational(1, 4)),
+         (Qubit('1011')/sqrt(2) + Qubit('1111')/sqrt(2), S.Half)]
+    assert measure_partial(state2, (0,)) == \
+        [(Qubit('1000'), Rational(1, 4)),
+         (Qubit('1111')/sqrt(3) + Qubit('1101')/sqrt(3) +
+          Qubit('1011')/sqrt(3), Rational(3, 4))]
+
+
+def test_measure_all():
+    assert measure_all(Qubit('11')) == [(Qubit('11'), 1)]
+    state = Qubit('11') + Qubit('10')
+    assert measure_all(state) == [(Qubit('10'), S.Half),
+           (Qubit('11'), S.Half)]
+    state2 = Qubit('11')/sqrt(5) + 2*Qubit('00')/sqrt(5)
+    assert measure_all(state2) == \
+        [(Qubit('00'), Rational(4, 5)), (Qubit('11'), Rational(1, 5))]
+
+    # from issue #12585
+    assert measure_all(qapply(Qubit('0'))) == [(Qubit('0'), 1)]
+
+
+def test_eval_trace():
+    q1 = Qubit('10110')
+    q2 = Qubit('01010')
+    d = Density([q1, 0.6], [q2, 0.4])
+
+    t = Tr(d)
+    assert t.doit() == 1.0
+
+    # extreme bits
+    t = Tr(d, 0)
+    assert t.doit() == (0.4*Density([Qubit('0101'), 1]) +
+                        0.6*Density([Qubit('1011'), 1]))
+    t = Tr(d, 4)
+    assert t.doit() == (0.4*Density([Qubit('1010'), 1]) +
+                        0.6*Density([Qubit('0110'), 1]))
+    # index somewhere in between
+    t = Tr(d, 2)
+    assert t.doit() == (0.4*Density([Qubit('0110'), 1]) +
+                        0.6*Density([Qubit('1010'), 1]))
+    #trace all indices
+    t = Tr(d, [0, 1, 2, 3, 4])
+    assert t.doit() == 1.0
+
+    # trace some indices, initialized in
+    # non-canonical order
+    t = Tr(d, [2, 1, 3])
+    assert t.doit() == (0.4*Density([Qubit('00'), 1]) +
+                        0.6*Density([Qubit('10'), 1]))
+
+    # mixed states
+    q = (1/sqrt(2)) * (Qubit('00') + Qubit('11'))
+    d = Density( [q, 1.0] )
+    t = Tr(d, 0)
+    assert t.doit() == (0.5*Density([Qubit('0'), 1]) +
+                        0.5*Density([Qubit('1'), 1]))
+
+
+def test_matrix_to_density():
+    mat = Matrix([[0, 0], [0, 1]])
+    assert matrix_to_density(mat) == Density([Qubit('1'), 1])
+
+    mat = Matrix([[1, 0], [0, 0]])
+    assert matrix_to_density(mat) == Density([Qubit('0'), 1])
+
+    mat = Matrix([[0, 0], [0, 0]])
+    assert matrix_to_density(mat) == 0
+
+    mat = Matrix([[0, 0, 0, 0],
+                  [0, 0, 0, 0],
+                  [0, 0, 1, 0],
+                  [0, 0, 0, 0]])
+
+    assert matrix_to_density(mat) == Density([Qubit('10'), 1])
+
+    mat = Matrix([[1, 0, 0, 0],
+                  [0, 0, 0, 0],
+                  [0, 0, 0, 0],
+                  [0, 0, 0, 0]])
+
+    assert matrix_to_density(mat) == Density([Qubit('00'), 1])

rl/Lib/site-packages/sympy/physics/quantum/tests/test_represent.py

@@ -0,0 +1,186 @@
+from sympy.core.numbers import (Float, I, Integer)
+from sympy.matrices.dense import Matrix
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.represent import (represent, rep_innerproduct,
+                                             rep_expectation, enumerate_states)
+from sympy.physics.quantum.state import Bra, Ket
+from sympy.physics.quantum.operator import Operator, OuterProduct
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.tensorproduct import matrix_tensor_product
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.matrixutils import (numpy_ndarray,
+                                               scipy_sparse_matrix, to_numpy,
+                                               to_scipy_sparse, to_sympy)
+from sympy.physics.quantum.cartesian import XKet, XOp, XBra
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.operatorset import operators_to_state
+from sympy.testing.pytest import raises
+
+Amat = Matrix([[1, I], [-I, 1]])
+Bmat = Matrix([[1, 2], [3, 4]])
+Avec = Matrix([[1], [I]])
+
+
+class AKet(Ket):
+
+    @classmethod
+    def dual_class(self):
+        return ABra
+
+    def _represent_default_basis(self, **options):
+        return self._represent_AOp(None, **options)
+
+    def _represent_AOp(self, basis, **options):
+        return Avec
+
+
+class ABra(Bra):
+
+    @classmethod
+    def dual_class(self):
+        return AKet
+
+
+class AOp(Operator):
+
+    def _represent_default_basis(self, **options):
+        return self._represent_AOp(None, **options)
+
+    def _represent_AOp(self, basis, **options):
+        return Amat
+
+
+class BOp(Operator):
+
+    def _represent_default_basis(self, **options):
+        return self._represent_AOp(None, **options)
+
+    def _represent_AOp(self, basis, **options):
+        return Bmat
+
+
+k = AKet('a')
+b = ABra('a')
+A = AOp('A')
+B = BOp('B')
+
+_tests = [
+    # Bra
+    (b, Dagger(Avec)),
+    (Dagger(b), Avec),
+    # Ket
+    (k, Avec),
+    (Dagger(k), Dagger(Avec)),
+    # Operator
+    (A, Amat),
+    (Dagger(A), Dagger(Amat)),
+    # OuterProduct
+    (OuterProduct(k, b), Avec*Avec.H),
+    # TensorProduct
+    (TensorProduct(A, B), matrix_tensor_product(Amat, Bmat)),
+    # Pow
+    (A**2, Amat**2),
+    # Add/Mul
+    (A*B + 2*A, Amat*Bmat + 2*Amat),
+    # Commutator
+    (Commutator(A, B), Amat*Bmat - Bmat*Amat),
+    # AntiCommutator
+    (AntiCommutator(A, B), Amat*Bmat + Bmat*Amat),
+    # InnerProduct
+    (InnerProduct(b, k), (Avec.H*Avec)[0])
+]
+
+
+def test_format_sympy():
+    for test in _tests:
+        lhs = represent(test[0], basis=A, format='sympy')
+        rhs = to_sympy(test[1])
+        assert lhs == rhs
+
+
+def test_scalar_sympy():
+    assert represent(Integer(1)) == Integer(1)
+    assert represent(Float(1.0)) == Float(1.0)
+    assert represent(1.0 + I) == 1.0 + I
+
+
+np = import_module('numpy')
+
+
+def test_format_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    for test in _tests:
+        lhs = represent(test[0], basis=A, format='numpy')
+        rhs = to_numpy(test[1])
+        if isinstance(lhs, numpy_ndarray):
+            assert (lhs == rhs).all()
+        else:
+            assert lhs == rhs
+
+
+def test_scalar_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    assert represent(Integer(1), format='numpy') == 1
+    assert represent(Float(1.0), format='numpy') == 1.0
+    assert represent(1.0 + I, format='numpy') == 1.0 + 1.0j
+
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def test_format_scipy_sparse():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+
+    for test in _tests:
+        lhs = represent(test[0], basis=A, format='scipy.sparse')
+        rhs = to_scipy_sparse(test[1])
+        if isinstance(lhs, scipy_sparse_matrix):
+            assert np.linalg.norm((lhs - rhs).todense()) == 0.0
+        else:
+            assert lhs == rhs
+
+
+def test_scalar_scipy_sparse():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+
+    assert represent(Integer(1), format='scipy.sparse') == 1
+    assert represent(Float(1.0), format='scipy.sparse') == 1.0
+    assert represent(1.0 + I, format='scipy.sparse') == 1.0 + 1.0j
+
+x_ket = XKet('x')
+x_bra = XBra('x')
+x_op = XOp('X')
+
+
+def test_innerprod_represent():
+    assert rep_innerproduct(x_ket) == InnerProduct(XBra("x_1"), x_ket).doit()
+    assert rep_innerproduct(x_bra) == InnerProduct(x_bra, XKet("x_1")).doit()
+    raises(TypeError, lambda: rep_innerproduct(x_op))
+
+
+def test_operator_represent():
+    basis_kets = enumerate_states(operators_to_state(x_op), 1, 2)
+    assert rep_expectation(
+        x_op) == qapply(basis_kets[1].dual*x_op*basis_kets[0])
+
+
+def test_enumerate_states():
+    test = XKet("foo")
+    assert enumerate_states(test, 1, 1) == [XKet("foo_1")]
+    assert enumerate_states(
+        test, [1, 2, 4]) == [XKet("foo_1"), XKet("foo_2"), XKet("foo_4")]

rl/Lib/site-packages/sympy/physics/quantum/tests/test_sho1d.py

@@ -0,0 +1,120 @@
+"""Tests for sho1d.py"""
+
+from sympy.core.numbers import (I, Integer)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum import Dagger
+from sympy.physics.quantum.constants import hbar
+from sympy.physics.quantum import Commutator
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.cartesian import X, Px
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.physics.quantum.hilbert import ComplexSpace
+from sympy.physics.quantum.represent import represent
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+from sympy.physics.quantum.sho1d import (RaisingOp, LoweringOp,
+                                        SHOKet, SHOBra,
+                                        Hamiltonian, NumberOp)
+
+ad = RaisingOp('a')
+a = LoweringOp('a')
+k = SHOKet('k')
+kz = SHOKet(0)
+kf = SHOKet(1)
+k3 = SHOKet(3)
+b = SHOBra('b')
+b3 = SHOBra(3)
+H = Hamiltonian('H')
+N = NumberOp('N')
+omega = Symbol('omega')
+m = Symbol('m')
+ndim = Integer(4)
+
+np = import_module('numpy')
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+ad_rep_sympy = represent(ad, basis=N, ndim=4, format='sympy')
+a_rep = represent(a, basis=N, ndim=4, format='sympy')
+N_rep = represent(N, basis=N, ndim=4, format='sympy')
+H_rep = represent(H, basis=N, ndim=4, format='sympy')
+k3_rep = represent(k3, basis=N, ndim=4, format='sympy')
+b3_rep = represent(b3, basis=N, ndim=4, format='sympy')
+
+def test_RaisingOp():
+    assert Dagger(ad) == a
+    assert Commutator(ad, a).doit() == Integer(-1)
+    assert Commutator(ad, N).doit() == Integer(-1)*ad
+    assert qapply(ad*k) == (sqrt(k.n + 1)*SHOKet(k.n + 1)).expand()
+    assert qapply(ad*kz) == (sqrt(kz.n + 1)*SHOKet(kz.n + 1)).expand()
+    assert qapply(ad*kf) == (sqrt(kf.n + 1)*SHOKet(kf.n + 1)).expand()
+    assert ad.rewrite('xp').doit() == \
+        (Integer(1)/sqrt(Integer(2)*hbar*m*omega))*(Integer(-1)*I*Px + m*omega*X)
+    assert ad.hilbert_space == ComplexSpace(S.Infinity)
+    for i in range(ndim - 1):
+        assert ad_rep_sympy[i + 1,i] == sqrt(i + 1)
+
+    if not np:
+        skip("numpy not installed.")
+
+    ad_rep_numpy = represent(ad, basis=N, ndim=4, format='numpy')
+    for i in range(ndim - 1):
+        assert ad_rep_numpy[i + 1,i] == float(sqrt(i + 1))
+
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+
+    ad_rep_scipy = represent(ad, basis=N, ndim=4, format='scipy.sparse', spmatrix='lil')
+    for i in range(ndim - 1):
+        assert ad_rep_scipy[i + 1,i] == float(sqrt(i + 1))
+
+    assert ad_rep_numpy.dtype == 'float64'
+    assert ad_rep_scipy.dtype == 'float64'
+
+def test_LoweringOp():
+    assert Dagger(a) == ad
+    assert Commutator(a, ad).doit() == Integer(1)
+    assert Commutator(a, N).doit() == a
+    assert qapply(a*k) == (sqrt(k.n)*SHOKet(k.n-Integer(1))).expand()
+    assert qapply(a*kz) == Integer(0)
+    assert qapply(a*kf) == (sqrt(kf.n)*SHOKet(kf.n-Integer(1))).expand()
+    assert a.rewrite('xp').doit() == \
+        (Integer(1)/sqrt(Integer(2)*hbar*m*omega))*(I*Px + m*omega*X)
+    for i in range(ndim - 1):
+        assert a_rep[i,i + 1] == sqrt(i + 1)
+
+def test_NumberOp():
+    assert Commutator(N, ad).doit() == ad
+    assert Commutator(N, a).doit() == Integer(-1)*a
+    assert Commutator(N, H).doit() == Integer(0)
+    assert qapply(N*k) == (k.n*k).expand()
+    assert N.rewrite('a').doit() == ad*a
+    assert N.rewrite('xp').doit() == (Integer(1)/(Integer(2)*m*hbar*omega))*(
+        Px**2 + (m*omega*X)**2) - Integer(1)/Integer(2)
+    assert N.rewrite('H').doit() == H/(hbar*omega) - Integer(1)/Integer(2)
+    for i in range(ndim):
+        assert N_rep[i,i] == i
+    assert N_rep == ad_rep_sympy*a_rep
+
+def test_Hamiltonian():
+    assert Commutator(H, N).doit() == Integer(0)
+    assert qapply(H*k) == ((hbar*omega*(k.n + Integer(1)/Integer(2)))*k).expand()
+    assert H.rewrite('a').doit() == hbar*omega*(ad*a + Integer(1)/Integer(2))
+    assert H.rewrite('xp').doit() == \
+        (Integer(1)/(Integer(2)*m))*(Px**2 + (m*omega*X)**2)
+    assert H.rewrite('N').doit() == hbar*omega*(N + Integer(1)/Integer(2))
+    for i in range(ndim):
+        assert H_rep[i,i] == hbar*omega*(i + Integer(1)/Integer(2))
+
+def test_SHOKet():
+    assert SHOKet('k').dual_class() == SHOBra
+    assert SHOBra('b').dual_class() == SHOKet
+    assert InnerProduct(b,k).doit() == KroneckerDelta(k.n, b.n)
+    assert k.hilbert_space == ComplexSpace(S.Infinity)
+    assert k3_rep[k3.n, 0] == Integer(1)
+    assert b3_rep[0, b3.n] == Integer(1)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_shor.py

@@ -0,0 +1,21 @@
+from sympy.testing.pytest import XFAIL
+
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qubit import Qubit
+from sympy.physics.quantum.shor import CMod, getr
+
+
+@XFAIL
+def test_CMod():
+    assert qapply(CMod(4, 2, 2)*Qubit(0, 0, 1, 0, 0, 0, 0, 0)) == \
+        Qubit(0, 0, 1, 0, 0, 0, 0, 0)
+    assert qapply(CMod(5, 5, 7)*Qubit(0, 0, 1, 0, 0, 0, 0, 0, 0, 0)) == \
+        Qubit(0, 0, 1, 0, 0, 0, 0, 0, 1, 0)
+    assert qapply(CMod(3, 2, 3)*Qubit(0, 1, 0, 0, 0, 0)) == \
+        Qubit(0, 1, 0, 0, 0, 1)
+
+
+def test_continued_frac():
+    assert getr(513, 1024, 10) == 2
+    assert getr(169, 1024, 11) == 6
+    assert getr(314, 4096, 16) == 13

rl/Lib/site-packages/sympy/physics/quantum/tests/test_state.py

@@ -0,0 +1,248 @@
+from sympy.core.add import Add
+from sympy.core.function import diff
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer, Rational, oo, pi)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.testing.pytest import raises
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.state import (
+    Ket, Bra, TimeDepKet, TimeDepBra,
+    KetBase, BraBase, StateBase, Wavefunction,
+    OrthogonalKet, OrthogonalBra
+)
+from sympy.physics.quantum.hilbert import HilbertSpace
+
+x, y, t = symbols('x,y,t')
+
+
+class CustomKet(Ket):
+    @classmethod
+    def default_args(self):
+        return ("test",)
+
+
+class CustomKetMultipleLabels(Ket):
+    @classmethod
+    def default_args(self):
+        return ("r", "theta", "phi")
+
+
+class CustomTimeDepKet(TimeDepKet):
+    @classmethod
+    def default_args(self):
+        return ("test", "t")
+
+
+class CustomTimeDepKetMultipleLabels(TimeDepKet):
+    @classmethod
+    def default_args(self):
+        return ("r", "theta", "phi", "t")
+
+
+def test_ket():
+    k = Ket('0')
+
+    assert isinstance(k, Ket)
+    assert isinstance(k, KetBase)
+    assert isinstance(k, StateBase)
+    assert isinstance(k, QExpr)
+
+    assert k.label == (Symbol('0'),)
+    assert k.hilbert_space == HilbertSpace()
+    assert k.is_commutative is False
+
+    # Make sure this doesn't get converted to the number pi.
+    k = Ket('pi')
+    assert k.label == (Symbol('pi'),)
+
+    k = Ket(x, y)
+    assert k.label == (x, y)
+    assert k.hilbert_space == HilbertSpace()
+    assert k.is_commutative is False
+
+    assert k.dual_class() == Bra
+    assert k.dual == Bra(x, y)
+    assert k.subs(x, y) == Ket(y, y)
+
+    k = CustomKet()
+    assert k == CustomKet("test")
+
+    k = CustomKetMultipleLabels()
+    assert k == CustomKetMultipleLabels("r", "theta", "phi")
+
+    assert Ket() == Ket('psi')
+
+
+def test_bra():
+    b = Bra('0')
+
+    assert isinstance(b, Bra)
+    assert isinstance(b, BraBase)
+    assert isinstance(b, StateBase)
+    assert isinstance(b, QExpr)
+
+    assert b.label == (Symbol('0'),)
+    assert b.hilbert_space == HilbertSpace()
+    assert b.is_commutative is False
+
+    # Make sure this doesn't get converted to the number pi.
+    b = Bra('pi')
+    assert b.label == (Symbol('pi'),)
+
+    b = Bra(x, y)
+    assert b.label == (x, y)
+    assert b.hilbert_space == HilbertSpace()
+    assert b.is_commutative is False
+
+    assert b.dual_class() == Ket
+    assert b.dual == Ket(x, y)
+    assert b.subs(x, y) == Bra(y, y)
+
+    assert Bra() == Bra('psi')
+
+
+def test_ops():
+    k0 = Ket(0)
+    k1 = Ket(1)
+    k = 2*I*k0 - (x/sqrt(2))*k1
+    assert k == Add(Mul(2, I, k0),
+        Mul(Rational(-1, 2), x, Pow(2, S.Half), k1))
+
+
+def test_time_dep_ket():
+    k = TimeDepKet(0, t)
+
+    assert isinstance(k, TimeDepKet)
+    assert isinstance(k, KetBase)
+    assert isinstance(k, StateBase)
+    assert isinstance(k, QExpr)
+
+    assert k.label == (Integer(0),)
+    assert k.args == (Integer(0), t)
+    assert k.time == t
+
+    assert k.dual_class() == TimeDepBra
+    assert k.dual == TimeDepBra(0, t)
+
+    assert k.subs(t, 2) == TimeDepKet(0, 2)
+
+    k = TimeDepKet(x, 0.5)
+    assert k.label == (x,)
+    assert k.args == (x, sympify(0.5))
+
+    k = CustomTimeDepKet()
+    assert k.label == (Symbol("test"),)
+    assert k.time == Symbol("t")
+    assert k == CustomTimeDepKet("test", "t")
+
+    k = CustomTimeDepKetMultipleLabels()
+    assert k.label == (Symbol("r"), Symbol("theta"), Symbol("phi"))
+    assert k.time == Symbol("t")
+    assert k == CustomTimeDepKetMultipleLabels("r", "theta", "phi", "t")
+
+    assert TimeDepKet() == TimeDepKet("psi", "t")
+
+
+def test_time_dep_bra():
+    b = TimeDepBra(0, t)
+
+    assert isinstance(b, TimeDepBra)
+    assert isinstance(b, BraBase)
+    assert isinstance(b, StateBase)
+    assert isinstance(b, QExpr)
+
+    assert b.label == (Integer(0),)
+    assert b.args == (Integer(0), t)
+    assert b.time == t
+
+    assert b.dual_class() == TimeDepKet
+    assert b.dual == TimeDepKet(0, t)
+
+    k = TimeDepBra(x, 0.5)
+    assert k.label == (x,)
+    assert k.args == (x, sympify(0.5))
+
+    assert TimeDepBra() == TimeDepBra("psi", "t")
+
+
+def test_bra_ket_dagger():
+    x = symbols('x', complex=True)
+    k = Ket('k')
+    b = Bra('b')
+    assert Dagger(k) == Bra('k')
+    assert Dagger(b) == Ket('b')
+    assert Dagger(k).is_commutative is False
+
+    k2 = Ket('k2')
+    e = 2*I*k + x*k2
+    assert Dagger(e) == conjugate(x)*Dagger(k2) - 2*I*Dagger(k)
+
+
+def test_wavefunction():
+    x, y = symbols('x y', real=True)
+    L = symbols('L', positive=True)
+    n = symbols('n', integer=True, positive=True)
+
+    f = Wavefunction(x**2, x)
+    p = f.prob()
+    lims = f.limits
+
+    assert f.is_normalized is False
+    assert f.norm is oo
+    assert f(10) == 100
+    assert p(10) == 10000
+    assert lims[x] == (-oo, oo)
+    assert diff(f, x) == Wavefunction(2*x, x)
+    raises(NotImplementedError, lambda: f.normalize())
+    assert conjugate(f) == Wavefunction(conjugate(f.expr), x)
+    assert conjugate(f) == Dagger(f)
+
+    g = Wavefunction(x**2*y + y**2*x, (x, 0, 1), (y, 0, 2))
+    lims_g = g.limits
+
+    assert lims_g[x] == (0, 1)
+    assert lims_g[y] == (0, 2)
+    assert g.is_normalized is False
+    assert g.norm == sqrt(42)/3
+    assert g(2, 4) == 0
+    assert g(1, 1) == 2
+    assert diff(diff(g, x), y) == Wavefunction(2*x + 2*y, (x, 0, 1), (y, 0, 2))
+    assert conjugate(g) == Wavefunction(conjugate(g.expr), *g.args[1:])
+    assert conjugate(g) == Dagger(g)
+
+    h = Wavefunction(sqrt(5)*x**2, (x, 0, 1))
+    assert h.is_normalized is True
+    assert h.normalize() == h
+    assert conjugate(h) == Wavefunction(conjugate(h.expr), (x, 0, 1))
+    assert conjugate(h) == Dagger(h)
+
+    piab = Wavefunction(sin(n*pi*x/L), (x, 0, L))
+    assert piab.norm == sqrt(L/2)
+    assert piab(L + 1) == 0
+    assert piab(0.5) == sin(0.5*n*pi/L)
+    assert piab(0.5, n=1, L=1) == sin(0.5*pi)
+    assert piab.normalize() == \
+        Wavefunction(sqrt(2)/sqrt(L)*sin(n*pi*x/L), (x, 0, L))
+    assert conjugate(piab) == Wavefunction(conjugate(piab.expr), (x, 0, L))
+    assert conjugate(piab) == Dagger(piab)
+
+    k = Wavefunction(x**2, 'x')
+    assert type(k.variables[0]) == Symbol
+
+def test_orthogonal_states():
+    braket = OrthogonalBra(x) * OrthogonalKet(x)
+    assert braket.doit() == 1
+
+    braket = OrthogonalBra(x) * OrthogonalKet(x+1)
+    assert braket.doit() == 0
+
+    braket = OrthogonalBra(x) * OrthogonalKet(y)
+    assert braket.doit() == braket

rl/Lib/site-packages/sympy/physics/quantum/tests/test_tensorproduct.py

@@ -0,0 +1,137 @@
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.core.expr import unchanged
+from sympy.matrices import Matrix, SparseMatrix, ImmutableMatrix
+
+from sympy.physics.quantum.commutator import Commutator as Comm
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.tensorproduct import TensorProduct as TP
+from sympy.physics.quantum.tensorproduct import tensor_product_simp
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.qubit import Qubit, QubitBra
+from sympy.physics.quantum.operator import OuterProduct
+from sympy.physics.quantum.density import Density
+from sympy.physics.quantum.trace import Tr
+
+A, B, C, D = symbols('A,B,C,D', commutative=False)
+x = symbols('x')
+
+mat1 = Matrix([[1, 2*I], [1 + I, 3]])
+mat2 = Matrix([[2*I, 3], [4*I, 2]])
+
+
+def test_sparse_matrices():
+    spm = SparseMatrix.diag(1, 0)
+    assert unchanged(TensorProduct, spm, spm)
+
+
+def test_tensor_product_dagger():
+    assert Dagger(TensorProduct(I*A, B)) == \
+        -I*TensorProduct(Dagger(A), Dagger(B))
+    assert Dagger(TensorProduct(mat1, mat2)) == \
+        TensorProduct(Dagger(mat1), Dagger(mat2))
+
+
+def test_tensor_product_abstract():
+
+    assert TP(x*A, 2*B) == x*2*TP(A, B)
+    assert TP(A, B) != TP(B, A)
+    assert TP(A, B).is_commutative is False
+    assert isinstance(TP(A, B), TP)
+    assert TP(A, B).subs(A, C) == TP(C, B)
+
+
+def test_tensor_product_expand():
+    assert TP(A + B, B + C).expand(tensorproduct=True) == \
+        TP(A, B) + TP(A, C) + TP(B, B) + TP(B, C)
+    #Tests for fix of issue #24142
+    assert TP(A-B, B-A).expand(tensorproduct=True) == \
+        TP(A, B) - TP(A, A) - TP(B, B) + TP(B, A)
+    assert TP(2*A + B, A + B).expand(tensorproduct=True) == \
+        2 * TP(A, A) + 2 * TP(A, B) + TP(B, A) + TP(B, B)
+    assert TP(2 * A * B + A, A + B).expand(tensorproduct=True) == \
+        2 * TP(A*B, A) + 2 * TP(A*B, B) + TP(A, A) + TP(A, B)
+
+
+def test_tensor_product_commutator():
+    assert TP(Comm(A, B), C).doit().expand(tensorproduct=True) == \
+        TP(A*B, C) - TP(B*A, C)
+    assert Comm(TP(A, B), TP(B, C)).doit() == \
+        TP(A, B)*TP(B, C) - TP(B, C)*TP(A, B)
+
+
+def test_tensor_product_simp():
+    assert tensor_product_simp(TP(A, B)*TP(B, C)) == TP(A*B, B*C)
+    # tests for Pow-expressions
+    assert tensor_product_simp(TP(A, B)**x) == TP(A**x, B**x)
+    assert tensor_product_simp(x*TP(A, B)**2) == x*TP(A**2,B**2)
+    assert tensor_product_simp(x*(TP(A, B)**2)*TP(C,D)) == x*TP(A**2*C,B**2*D)
+    assert tensor_product_simp(TP(A,B)-TP(C,D)**x) == TP(A,B)-TP(C**x,D**x)
+
+
+def test_issue_5923():
+    # most of the issue regarding sympification of args has been handled
+    # and is tested internally by the use of args_cnc through the quantum
+    # module, but the following is a test from the issue that used to raise.
+    assert TensorProduct(1, Qubit('1')*Qubit('1').dual) == \
+        TensorProduct(1, OuterProduct(Qubit(1), QubitBra(1)))
+
+
+def test_eval_trace():
+    # This test includes tests with dependencies between TensorProducts
+    #and density operators. Since, the test is more to test the behavior of
+    #TensorProducts it remains here
+
+    A, B, C, D, E, F = symbols('A B C D E F', commutative=False)
+
+    # Density with simple tensor products as args
+    t = TensorProduct(A, B)
+    d = Density([t, 1.0])
+    tr = Tr(d)
+    assert tr.doit() == 1.0*Tr(A*Dagger(A))*Tr(B*Dagger(B))
+
+    ## partial trace with simple tensor products as args
+    t = TensorProduct(A, B, C)
+    d = Density([t, 1.0])
+    tr = Tr(d, [1])
+    assert tr.doit() == 1.0*A*Dagger(A)*Tr(B*Dagger(B))*C*Dagger(C)
+
+    tr = Tr(d, [0, 2])
+    assert tr.doit() == 1.0*Tr(A*Dagger(A))*B*Dagger(B)*Tr(C*Dagger(C))
+
+    # Density with multiple Tensorproducts as states
+    t2 = TensorProduct(A, B)
+    t3 = TensorProduct(C, D)
+
+    d = Density([t2, 0.5], [t3, 0.5])
+    t = Tr(d)
+    assert t.doit() == (0.5*Tr(A*Dagger(A))*Tr(B*Dagger(B)) +
+                        0.5*Tr(C*Dagger(C))*Tr(D*Dagger(D)))
+
+    t = Tr(d, [0])
+    assert t.doit() == (0.5*Tr(A*Dagger(A))*B*Dagger(B) +
+                        0.5*Tr(C*Dagger(C))*D*Dagger(D))
+
+    #Density with mixed states
+    d = Density([t2 + t3, 1.0])
+    t = Tr(d)
+    assert t.doit() == ( 1.0*Tr(A*Dagger(A))*Tr(B*Dagger(B)) +
+                        1.0*Tr(A*Dagger(C))*Tr(B*Dagger(D)) +
+                        1.0*Tr(C*Dagger(A))*Tr(D*Dagger(B)) +
+                        1.0*Tr(C*Dagger(C))*Tr(D*Dagger(D)))
+
+    t = Tr(d, [1] )
+    assert t.doit() == ( 1.0*A*Dagger(A)*Tr(B*Dagger(B)) +
+                        1.0*A*Dagger(C)*Tr(B*Dagger(D)) +
+                        1.0*C*Dagger(A)*Tr(D*Dagger(B)) +
+                        1.0*C*Dagger(C)*Tr(D*Dagger(D)))
+
+
+def test_pr24993():
+    from sympy.matrices.expressions.kronecker import matrix_kronecker_product
+    from sympy.physics.quantum.matrixutils    import matrix_tensor_product
+    X = Matrix([[0, 1], [1, 0]])
+    Xi = ImmutableMatrix(X)
+    assert TensorProduct(Xi, Xi) == TensorProduct(X, X)
+    assert TensorProduct(Xi, Xi) == matrix_tensor_product(X, X)
+    assert TensorProduct(Xi, Xi) == matrix_kronecker_product(X, X)

rl/Lib/site-packages/sympy/physics/quantum/tests/test_trace.py

@@ -0,0 +1,109 @@
+from sympy.core.containers import Tuple
+from sympy.core.symbol import symbols
+from sympy.matrices.dense import Matrix
+from sympy.physics.quantum.trace import Tr
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+def test_trace_new():
+    a, b, c, d, Y = symbols('a b c d Y')
+    A, B, C, D = symbols('A B C D', commutative=False)
+
+    assert Tr(a + b) == a + b
+    assert Tr(A + B) == Tr(A) + Tr(B)
+
+    #check trace args not implicitly permuted
+    assert Tr(C*D*A*B).args[0].args == (C, D, A, B)
+
+    # check for mul and adds
+    assert Tr((a*b) + ( c*d)) == (a*b) + (c*d)
+    # Tr(scalar*A) = scalar*Tr(A)
+    assert Tr(a*A) == a*Tr(A)
+    assert Tr(a*A*B*b) == a*b*Tr(A*B)
+
+    # since A is symbol and not commutative
+    assert isinstance(Tr(A), Tr)
+
+    #POW
+    assert Tr(pow(a, b)) == a**b
+    assert isinstance(Tr(pow(A, a)), Tr)
+
+    #Matrix
+    M = Matrix([[1, 1], [2, 2]])
+    assert Tr(M) == 3
+
+    ##test indices in different forms
+    #no index
+    t = Tr(A)
+    assert t.args[1] == Tuple()
+
+    #single index
+    t = Tr(A, 0)
+    assert t.args[1] == Tuple(0)
+
+    #index in a list
+    t = Tr(A, [0])
+    assert t.args[1] == Tuple(0)
+
+    t = Tr(A, [0, 1, 2])
+    assert t.args[1] == Tuple(0, 1, 2)
+
+    #index is tuple
+    t = Tr(A, (0))
+    assert t.args[1] == Tuple(0)
+
+    t = Tr(A, (1, 2))
+    assert t.args[1] == Tuple(1, 2)
+
+    #trace indices test
+    t = Tr((A + B), [2])
+    assert t.args[0].args[1] == Tuple(2) and t.args[1].args[1] == Tuple(2)
+
+    t = Tr(a*A, [2, 3])
+    assert t.args[1].args[1] == Tuple(2, 3)
+
+    #class with trace method defined
+    #to simulate numpy objects
+    class Foo:
+        def trace(self):
+            return 1
+    assert Tr(Foo()) == 1
+
+    #argument test
+    # check for value error, when either/both arguments are not provided
+    raises(ValueError, lambda: Tr())
+    raises(ValueError, lambda: Tr(A, 1, 2))
+
+
+def test_trace_doit():
+    a, b, c, d = symbols('a b c d')
+    A, B, C, D = symbols('A B C D', commutative=False)
+
+    #TODO: needed while testing reduced density operations, etc.
+
+
+def test_permute():
+    A, B, C, D, E, F, G = symbols('A B C D E F G', commutative=False)
+    t = Tr(A*B*C*D*E*F*G)
+
+    assert t.permute(0).args[0].args == (A, B, C, D, E, F, G)
+    assert t.permute(2).args[0].args == (F, G, A, B, C, D, E)
+    assert t.permute(4).args[0].args == (D, E, F, G, A, B, C)
+    assert t.permute(6).args[0].args == (B, C, D, E, F, G, A)
+    assert t.permute(8).args[0].args == t.permute(1).args[0].args
+
+    assert t.permute(-1).args[0].args == (B, C, D, E, F, G, A)
+    assert t.permute(-3).args[0].args == (D, E, F, G, A, B, C)
+    assert t.permute(-5).args[0].args == (F, G, A, B, C, D, E)
+    assert t.permute(-8).args[0].args == t.permute(-1).args[0].args
+
+    t = Tr((A + B)*(B*B)*C*D)
+    assert t.permute(2).args[0].args == (C, D, (A + B), (B**2))
+
+    t1 = Tr(A*B)
+    t2 = t1.permute(1)
+    assert id(t1) != id(t2) and t1 == t2
+
+def test_deprecated_core_trace():
+    with warns_deprecated_sympy():
+        from sympy.core.trace import Tr # noqa:F401