def test_depolarizing() -> None:
p = 1.0 - np.exp(-1 / 20)
chan = qf.Depolarizing(p, 0).aschannel()
rho0 = qf.Density([[0.5, 0], [0, 0.5]])
assert qf.densities_close(rho0, chan.evolve(rho0))
rho0 = qf.random_density(1)
rho1 = chan.evolve(rho0)
pr0 = np.real(qf.purity(rho0))
pr1 = np.real(qf.purity(rho1))
assert pr0 > pr1
# Test data extracted from refereneqvm
rho2 = qf.Density([[0.43328691, 0.48979689], [0.48979689, 0.56671309]])
rho_test = qf.Density(
[[0.43762509 + 0.0j, 0.45794666 + 0.0j], [0.45794666 + 0.0j, 0.56237491 + 0.0j]]
)
assert qf.densities_close(chan.evolve(rho2), rho_test)
ket0 = qf.random_state(1)
qf.Depolarizing(p, 0).run(ket0)
rho1b = qf.Depolarizing(p, 0).evolve(rho0)
assert qf.densities_close(rho1, rho1b)
def test_density():
ket = qf.random_state(3)
matrix = bk.outer(ket.tensor, bk.conj(ket.tensor))
qf.Density(matrix)
qf.Density(matrix, [0, 1, 2])
with pytest.raises(ValueError):
qf.Density(matrix, [0, 1, 2, 3])
def test_density() -> None:
ket = qf.random_state(3)
matrix = qf.tensors.outer(ket.tensor, np.conj(ket.tensor), rank=1)
qf.Density(matrix)
qf.Density(matrix, [0, 1, 2])
with pytest.raises(ValueError):
qf.Density(matrix, [0, 1, 2, 3])
def test_density():
ket = qf.random_state(3)
matrix = bk.outer(ket.tensor, bk.conj(ket.tensor))
qf.Density(matrix)
rho = qf.Density(matrix, [0, 1, 2])
with pytest.raises(ValueError):
qf.Density(matrix, [0, 1, 2, 3])
assert rho.asdensity() is rho
rho = rho.relabel([10, 11, 12]).permute([12, 11, 10])
assert rho.qubits == (12, 11, 10)
def test_density() -> None:
ket = qf.random_state(3)
matrix = np.outer(ket.tensor, np.conj(ket.tensor))
qf.Density(matrix)
rho = qf.Density(matrix, [0, 1, 2])
with pytest.raises(ValueError):
qf.Density(matrix, [0, 1, 2, 3])
assert rho.asdensity() is rho
rho = rho.on(10, 11, 12).permute([12, 11, 10])
assert rho.qubits == (12, 11, 10)
rho.permute()
def test_density_trace() -> None:
rho = qf.random_density(3)
assert np.isclose(rho.trace(), 1)
rho = qf.Density(np.eye(8))
assert np.isclose(rho.trace(), 8)
rho = rho.normalize()
assert np.isclose(rho.trace(), 1)
def test_density_trace():
rho = qf.random_density(3)
assert qf.asarray(rho.trace()) == ALMOST_ONE
rho = qf.Density(np.eye(8))
assert np.isclose(qf.asarray(rho.trace()), 8)
rho = rho.normalize()
assert np.isclose(qf.asarray(rho.trace()), 1)
def test_purity() -> None:
density = qf.ghz_state(4).asdensity()
assert np.isclose(qf.purity(density), 1.0)
for _ in range(10):
density = qf.random_density(4)
purity = np.real(qf.purity(density))
assert purity < 1.0
assert purity >= 0.0
rho = qf.Density(np.diag([0.9, 0.1]))
assert np.isclose(qf.purity(rho), 0.82) # Kudos: Josh Combs
def test_purity():
density = qf.ghz_state(4).asdensity()
assert qf.asarray(qf.purity(density)) == ALMOST_ONE
for _ in range(10):
density = qf.random_density(4)
purity = np.real(qf.asarray(qf.purity(density)))
assert purity < 1.0
assert purity >= 0.0
rho = qf.Density(np.diag([0.9, 0.1]))
assert np.isclose(qf.asarray(qf.purity(rho)), 0.82) # Kudos: Josh Combes
def test_amplitude_damping():
rho = qf.zero_state(1).asdensity()
p = 1.0 - np.exp(-(50) / 15000)
chan = qf.Damping(p, 0).aschannel()
rho1 = chan.evolve(rho)
assert qf.densities_close(rho, rho1)
rho2 = qf.X(0).aschannel().evolve(rho1)
rho3 = chan.evolve(rho2)
expected = qf.Density([[0.00332778 + 0.j, 0.00000000 + 0.j],
[0.00000000 + 0.j, 0.99667222 + 0.j]])
assert qf.densities_close(expected, rho3)
def test_kraus_evolve():
rho = qf.zero_state(1).asdensity()
p = 1 - np.exp(-50 / 15000)
kraus = qf.Damping(p, 0)
rho1 = kraus.evolve(rho)
assert qf.densities_close(rho, rho1)
rho2 = qf.X(0).aschannel().evolve(rho1)
rho3 = kraus.evolve(rho2)
expected = qf.Density([[0.00332778 + 0.j, 0.00000000 + 0.j],
[0.00000000 + 0.j, 0.99667222 + 0.j]])
assert qf.densities_close(expected, rho3)
def test_kraus_run():
ket0 = qf.zero_state(['a'])
ket0 = qf.X('a').run(ket0)
p = 1.0 - np.exp(-2000 / 15000)
kraus = qf.Damping(p, 'a')
reps = 1000
results = [kraus.run(ket0).asdensity().asoperator() for _ in range(reps)]
matrix = reduce(add, results) / reps
rho_kraus = qf.Density(matrix, ['a'])
rho0 = ket0.asdensity()
chan = kraus.aschannel()
rho_chan = chan.evolve(rho0)
# If this fails occasionally consider increasing tolerance
# Can't be very tolerant due to stochastic dynamics
assert qf.densities_close(rho_chan, rho_kraus, tolerance=0.05)
