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_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_eval_trace(): up = JzKet(S(1)/2,S(1)/2) down = JzKet(S(1)/2,-S(1)/2) d = Density((up,0.5),(down,0.5)) t = Tr(d) assert t.doit() == 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 # 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 # 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_eval_trace(): q1 = Qubit('10110') q2 = Qubit('01010') d = Density([q1, 0.6], [q2, 0.4]) t = Tr(d) assert t.doit() == 1 # 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 # 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_eval_trace(): up = JzKet(S(1)/2, S(1)/2) down = JzKet(S(1)/2, -S(1)/2) d = Density((up, 0.5), (down, 0.5)) t = Tr(d) assert t.doit() == 1 #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
def test_eval_trace(): up = JzKet(S(1) / 2, S(1) / 2) down = JzKet(S(1) / 2, -S(1) / 2) d = Density((up, 0.5), (down, 0.5)) t = Tr(d) assert t.doit() == 1 #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