def test_id_with_T1_T2(self):
"""
Test for identity evolution with relaxation t1 and t2
"""
# setup
a = destroy(2)
Hadamard = hadamard_transform(1)
ex_state = basis(2, 1)
mines_state = (basis(2, 1) - basis(2, 0)).unit()
end_time = 2.
tlist = np.arange(0, end_time + 0.02, 0.02)
t1 = 1.
t2 = 0.5
# test t1
test = Processor(1, t1=t1)
test.tlist = tlist
result = test.run_state(ex_state, e_ops=[a.dag() * a])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t1 * end_time),
rtol=1e-5,
err_msg="Error in t1 time simulation")
# test t2
test = Processor(1, t2=t2)
test.tlist = tlist
result = test.run_state(rho0=mines_state,
e_ops=[Hadamard * a.dag() * a * Hadamard])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t2 * end_time) * 0.5 + 0.5,
rtol=1e-5,
err_msg="Error in t2 time simulation")
# test t1 and t2
t1 = np.random.rand(1) + 0.5
t2 = np.random.rand(1) * 0.5 + 0.5
test = Processor(1, t1=t1, t2=t2)
test.tlist = tlist
result = test.run_state(rho0=mines_state,
e_ops=[Hadamard * a.dag() * a * Hadamard])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t2 * end_time) * 0.5 + 0.5,
rtol=1e-5,
err_msg="Error in t1 & t2 simulation, "
"with t1={} and t2={}".format(t1, t2))
def test_dnorm_qubit_known_cases():
"""
Metrics: check agreement for known qubit channels.
"""
def case(chan1, chan2, expected, significant=4):
# We again take a generous tolerance so that we don't kill off
# SCS solvers.
assert_approx_equal(dnorm(chan1, chan2),
expected,
significant=significant)
id_chan = to_choi(qeye(2))
S_eye = to_super(id_chan)
X_chan = to_choi(sigmax())
depol = to_choi(
Qobj(diag(ones((4, ))), dims=[[[2], [2]], [[2], [2]]], superrep='chi'))
S_H = to_super(hadamard_transform())
W = swap()
# We need to restrict the number of iterations for things on the boundary,
# such as perfectly distinguishable channels.
yield case, id_chan, X_chan, 2
yield case, id_chan, depol, 1.5
# Next, we'll generate some test cases based on comparisons to pre-existing
# dnorm() implementations. In particular, the targets for the following
# test cases were generated using QuantumUtils for MATLAB (https://goo.gl/oWXhO9).
def overrotation(x):
return to_super((1j * np.pi * x * sigmax() / 2).expm())
for x, target in {
1.000000e-03: 3.141591e-03,
3.100000e-03: 9.738899e-03,
1.000000e-02: 3.141463e-02,
3.100000e-02: 9.735089e-02,
1.000000e-01: 3.128689e-01,
3.100000e-01: 9.358596e-01
}.items():
yield case, overrotation(x), id_chan, target
def had_mixture(x):
return (1 - x) * S_eye + x * S_H
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.200000e-03,
1.000000e-02: 2.000000e-02,
3.100000e-02: 6.200000e-02,
1.000000e-01: 2.000000e-01,
3.100000e-01: 6.200000e-01
}.items():
yield case, had_mixture(x), id_chan, target
def swap_map(x):
S = (1j * x * W).expm()
S._type = None
S.dims = [[[2], [2]], [[2], [2]]]
S.superrep = 'super'
return S
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.199997e-03,
1.000000e-02: 1.999992e-02,
3.100000e-02: 6.199752e-02,
1.000000e-01: 1.999162e-01,
3.100000e-01: 6.173918e-01
}.items():
yield case, swap_map(x), id_chan, target
# Finally, we add a known case from Johnston's QETLAB documentation,
# || Phi - I ||,_♢ where Phi(X) = UXU⁺ and U = [[1, 1], [-1, 1]] / sqrt(2).
yield case, Qobj([[1, 1], [-1, 1]]) / np.sqrt(2), qeye(2), np.sqrt(2)
def test_dnorm_qubit_known_cases():
"""
Metrics: check agreement for known qubit channels.
"""
def case(chan1, chan2, expected, significant=4):
# We again take a generous tolerance so that we don't kill off
# SCS solvers.
assert_approx_equal(
dnorm(chan1, chan2), expected,
significant=significant
)
id_chan = to_choi(qeye(2))
S_eye = to_super(id_chan)
X_chan = to_choi(sigmax())
depol = to_choi(Qobj(
diag(ones((4,))),
dims=[[[2], [2]], [[2], [2]]], superrep='chi'
))
S_H = to_super(hadamard_transform())
W = swap()
# We need to restrict the number of iterations for things on the boundary,
# such as perfectly distinguishable channels.
yield case, id_chan, X_chan, 2
yield case, id_chan, depol, 1.5
# Next, we'll generate some test cases based on comparisons to pre-existing
# dnorm() implementations. In particular, the targets for the following
# test cases were generated using QuantumUtils for MATLAB (https://goo.gl/oWXhO9).
def overrotation(x):
return to_super((1j * np.pi * x * sigmax() / 2).expm())
for x, target in {
1.000000e-03: 3.141591e-03,
3.100000e-03: 9.738899e-03,
1.000000e-02: 3.141463e-02,
3.100000e-02: 9.735089e-02,
1.000000e-01: 3.128689e-01,
3.100000e-01: 9.358596e-01
}.items():
yield case, overrotation(x), id_chan, target
def had_mixture(x):
return (1 - x) * S_eye + x * S_H
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.200000e-03,
1.000000e-02: 2.000000e-02,
3.100000e-02: 6.200000e-02,
1.000000e-01: 2.000000e-01,
3.100000e-01: 6.200000e-01
}.items():
yield case, had_mixture(x), id_chan, target
def swap_map(x):
S = (1j * x * W).expm()
S._type = None
S.dims = [[[2], [2]], [[2], [2]]]
S.superrep = 'super'
return S
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.199997e-03,
1.000000e-02: 1.999992e-02,
3.100000e-02: 6.199752e-02,
1.000000e-01: 1.999162e-01,
3.100000e-01: 6.173918e-01
}.items():
yield case, swap_map(x), id_chan, target
# Finally, we add a known case from Johnston's QETLAB documentation,
# || Phi - I ||,_♢ where Phi(X) = UXU⁺ and U = [[1, 1], [-1, 1]] / sqrt(2).
yield case, Qobj([[1, 1], [-1, 1]]) / np.sqrt(2), qeye(2), np.sqrt(2)
print(qubit_states(N=2, states=[0, 0]))
print("\n")
x = sigmax()
print(x)
print("\n")
ket_zero = qubit_states(N=1, states=[0])
print(ket_zero)
print("\n")
print(x * ket_zero)
print("\n")
print(tensor([identity(N=2), hadamard_transform(N=1)]))
print("\n")
print(snot(N=2, target=1))
print("\n")
print(swap(N=2, targets=[0, 1]))
print("\n")
print(cnot(N=2, control=0, target=1))
print("\n")
print(cnot(N=4, control=0, target=3))
print("\n")
print(hadamard_transform(N=2) * qubit_states(N=2, states=[0, 0]))