def test_purity_standard():
rho0 = np.diag([1, 0])
rho1 = np.diag([0.9, 0.1])
rho2 = np.diag([0.5, 0.5])
assert dm.purity(rho0) == 1.0
assert np.allclose(dm.purity(rho1), 0.82) # by hand calc
assert dm.purity(rho2) == 0.5
rho_qutrit = np.diag([1.0, 1.0, 1.0]) / 3
assert dm.purity(rho_qutrit) == 1 / 3
def test_purity_renorm():
D = 2
rho0 = np.diag([1, 0])
rho1 = np.diag([0.9, 0.1])
rho2 = np.diag([0.5, 0.5])
assert dm.purity(rho0, dim_renorm=True) == 1.0
assert np.allclose(dm.purity(rho1, dim_renorm=True),
(D / (D - 1)) * (0.82 - 1 / D)) # by hand calc
assert dm.purity(rho2, dim_renorm=True) == 0.0
rho_qutrit = np.diag([1.0, 1.0, 1.0]) / 3
assert dm.purity(rho_qutrit, dim_renorm=True) == 0.0
def estimate_variance(
results: List[ExperimentResult],
qubits: List[int],
tomo_estimator: Callable,
functional: Callable,
target_state=None,
n_resamples: int = 40,
project_to_physical: bool = False) -> Tuple[float, float]:
"""
Use a simple bootstrap-like method to return an errorbar on some functional of the
quantum state.
:param results: Measured results from a state tomography experiment
:param qubits: Qubits that were tomographized.
:param tomo_estimator: takes in ``results, qubits`` and returns a corresponding
estimate of the state rho, e.g. ``linear_inv_state_estimate``
:param functional: Which functional to find variance, e.g. ``dm.purity``.
:param target_state: A density matrix of the state with respect to which the distance
functional is measured. Not applicable if functional is ``dm.purity``.
:param n_resamples: The number of times to resample.
:param project_to_physical: Whether to project the estimated state to a physical one
with :py:func:`project_density_matrix`.
"""
if functional != dm.purity:
if target_state is None:
raise ValueError("You're not using the `purity` functional. "
"Please specify a target state.")
sample_estimate = []
for _ in range(n_resamples):
resampled_results = _resample_expectations_with_beta(results)
estimate = tomo_estimator(resampled_results, qubits)
# TODO: Shim! over different return values between linear inv. and mle
if isinstance(estimate, np.ndarray):
rho = estimate
else:
rho = estimate.estimate.state_point_est
if project_to_physical:
rho = project_density_matrix(rho)
# Calculate functional of the state
if functional == dm.purity:
sample_estimate.append(np.real(dm.purity(rho, dim_renorm=False)))
else:
sample_estimate.append(np.real(functional(target_state, rho)))
return np.mean(sample_estimate), np.var(sample_estimate)