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
