def test_channel_process_fidelity(self):
"""Test the process_fidelity function for channel inputs"""
depol = Choi(np.eye(4) / 2)
iden = Choi(Operator.from_label('I'))
# Completely depolarizing channel
f_pro = process_fidelity(depol, require_cp=True, require_tp=True)
self.assertAlmostEqual(f_pro, 0.25, places=7)
# Identity
f_pro = process_fidelity(iden, require_cp=True, require_tp=True)
self.assertAlmostEqual(f_pro, 1.0, places=7)
# Depolarizing channel
prob = 0.3
chan = prob * depol + (1 - prob) * iden
f_pro = process_fidelity(chan, require_cp=True, require_tp=True)
f_target = prob * 0.25 + (1 - prob)
self.assertAlmostEqual(f_pro, f_target, places=7)
# Depolarizing channel
prob = 0.5
op = Operator.from_label('Y')
chan = (prob * depol + (1 - prob) * iden) @ op
f_pro = process_fidelity(chan, op, require_cp=True, require_tp=True)
target = prob * 0.25 + (1 - prob)
self.assertAlmostEqual(f_pro, target, places=7)
def test_channel_average_gate_fidelity(self):
"""Test the average_gate_fidelity function for channel inputs"""
depol = Choi(np.eye(4) / 2)
iden = Choi(Operator.from_label('I'))
# Completely depolarizing channel
f_ave = average_gate_fidelity(depol, require_cp=True, require_tp=True)
self.assertAlmostEqual(f_ave, 0.5, places=7)
# Identity
f_ave = average_gate_fidelity(iden, require_cp=True, require_tp=True)
self.assertAlmostEqual(f_ave, 1.0, places=7)
# Depolarizing channel
prob = 0.11
chan = prob * depol + (1 - prob) * iden
f_ave = average_gate_fidelity(chan, require_cp=True, require_tp=True)
f_target = (2 * (prob * 0.25 + (1 - prob)) + 1) / 3
self.assertAlmostEqual(f_ave, f_target, places=7)
# Depolarizing channel
prob = 0.5
op = Operator.from_label('Y')
chan = (prob * depol + (1 - prob) * iden).compose(op)
f_ave = average_gate_fidelity(chan,
op,
require_cp=True,
require_tp=True)
target = (2 * (prob * 0.25 + (1 - prob)) + 1) / 3
self.assertAlmostEqual(f_ave, target, places=7)
def _fidelity_result(
state_result: AnalysisResultData,
target: Union[Choi, DensityMatrix],
input_dim: int = 1,
):
"""Faster computation of fidelity from eigen decomposition"""
evals = state_result.extra["eigvals"]
evecs = state_result.extra["eigvecs"]
# Format target to statevector or densitymatrix array
name = "process_fidelity" if input_dim > 1 else "state_fidelity"
if target is None:
raise AnalysisError("No target state provided")
if isinstance(target, QuantumChannel):
target_state = Choi(target).data / input_dim
elif isinstance(target, BaseOperator):
target_state = np.ravel(Operator(target),
order="F") / np.sqrt(input_dim)
else:
# Statevector or density matrix
target_state = np.array(target)
if target_state.ndim == 1:
rho = evecs @ (evals / input_dim * evecs).T.conj()
fidelity = np.real(target_state.conj() @ rho @ target_state)
else:
sqrt_rho = evecs @ (np.sqrt(evals / input_dim) * evecs).T.conj()
eig = la.eigvalsh(sqrt_rho @ target_state @ sqrt_rho)
fidelity = np.sum(np.sqrt(np.maximum(eig, 0)))**2
return AnalysisResultData(name, fidelity)
def test_noncp_process_fidelity(self):
"""Test process_fidelity for non-CP channel"""
u1 = Operator.from_label('X')
u2 = Operator.from_label('Z')
chan = 1.01 * Choi(u1) - 0.01 * Choi(u2)
fid = process_fidelity(chan)
self.assertLogs('qiskit.quantum_info.operators.measures', level='WARNING')
self.assertAlmostEqual(fid, 0, places=15)
def _target_quantum_channel(self) -> Union[Choi, Operator]:
"""Return the process tomography target"""
# Check if circuit contains measure instructions
# If so we cannot return target state
circuit_ops = self._circuit.count_ops()
if "measure" in circuit_ops:
return None
try:
circuit = self._permute_circuit()
if "reset" in circuit_ops or "kraus" in circuit_ops or "superop" in circuit_ops:
channel = Choi(circuit)
else:
channel = Operator(circuit)
except QiskitError:
# Circuit couldn't be simulated
return None
total_qubits = self._circuit.num_qubits
num_meas = total_qubits if self._meas_qubits is None else len(self._meas_qubits)
num_prep = total_qubits if self._prep_qubits is None else len(self._prep_qubits)
# If all qubits are prepared or measurement we are done
if num_meas == total_qubits and num_prep == total_qubits:
return channel
# Convert channel to a state to project and trace out non-tomography
# input and output qubits
if isinstance(channel, Operator):
chan_state = Statevector(np.ravel(channel, order="F"))
else:
chan_state = DensityMatrix(channel.data)
# Get qargs for non measured and prepared subsystems
non_meas_qargs = list(range(num_meas, total_qubits))
non_prep_qargs = list(range(total_qubits + num_prep, 2 * total_qubits))
# Project non-prepared subsystems on to the zero state
if non_prep_qargs:
proj0 = Operator([[1, 0], [0, 0]])
for qarg in non_prep_qargs:
chan_state = chan_state.evolve(proj0, [qarg])
# Trace out indices to remove
tr_qargs = non_meas_qargs + non_prep_qargs
chan_state = partial_trace(chan_state, tr_qargs)
channel = Choi(chan_state.data, input_dims=[2] * num_prep, output_dims=[2] * num_meas)
return channel
def test_rank(self, rank):
"""Test random_quantum_channel with fixed rank {rank}"""
choi = Choi(random_quantum_channel(2, rank=rank))
# Get number of non-zero eigenvalues
evals = np.linalg.eigvals(choi.data).round(8)
value = len(evals[evals > 0])
self.assertEqual(value, rank)
def _join_input_vector(self,
E: np.array,
rho: np.array,
Gs: List[np.array]
) -> np.array:
"""Converts the GST data into a vector representation
Args:
E: The POVM measurement operator
rho: The initial state
Gs: The gates list
Returns:
The vector representation of (E, rho, Gs)
Additional information:
This function performs the inverse operation to
split_input_vector; the notations are the same.
"""
d = (2 ** self.qubits)
E_T = get_cholesky_like_decomposition(E.reshape((d, d)))
rho_T = get_cholesky_like_decomposition(rho.reshape((d, d)))
Gs_Choi = [Choi(PTM(G)).data for G in Gs]
Gs_T = [get_cholesky_like_decomposition(G) for G in Gs_Choi]
E_vec = self._complex_matrix_to_vec(E_T)
rho_vec = self._complex_matrix_to_vec(rho_T)
result = E_vec + rho_vec
for G_T in Gs_T:
result += self._complex_matrix_to_vec(G_T)
return np.array(result)
def test_nontp_process_fidelity(self):
"""Test process_fidelity for non-TP channel"""
chan = 0.99 * Choi(Operator.from_label('X'))
fid = process_fidelity(chan)
self.assertLogs('qiskit.quantum_info.operators.measures',
level='WARNING')
self.assertAlmostEqual(fid, 0, places=15)
def run_circuit_and_tomography(circuit, qubits, method):
choi_ideal = Choi(circuit).data
qst = tomo.process_tomography_circuits(circuit, qubits)
job = qiskit.execute(qst, Aer.get_backend('qasm_simulator'), shots=5000)
tomo_fit = tomo.ProcessTomographyFitter(job.result(), qst)
choi = tomo_fit.fit(method=method).data
return (choi, choi_ideal)
def test_channel_gate_error(self):
"""Test the gate_error function for channel inputs"""
depol = Choi(np.eye(4) / 2)
iden = Choi(Operator.from_label('I'))
# Depolarizing channel
prob = 0.11
chan = prob * depol + (1 - prob) * iden
err = gate_error(chan, require_cp=True, require_tp=True)
target = 1 - average_gate_fidelity(chan)
self.assertAlmostEqual(err, target, places=7)
# Depolarizing channel
prob = 0.5
op = Operator.from_label('Y')
chan = (prob * depol + (1 - prob) * iden) @ op
err = gate_error(chan, op, require_cp=True, require_tp=True)
target = 1 - average_gate_fidelity(chan, op)
self.assertAlmostEqual(err, target, places=7)
def test_diamond_norm(self, num_qubits):
"""Test the diamond_norm for {num_qubits}-qubit pauli channel."""
try:
import cvxpy
except ImportError:
# Skip test if CVXPY not installed
self.skipTest("CVXPY not installed.")
# Pauli channels have an analytic expression for the
# diamond norm so we can easily test it
op = Choi(np.zeros((4 ** num_qubits, 4 ** num_qubits)))
labels = [num_qubits * i for i in ['I', 'X', 'Y', 'Z']]
coeffs = [-1.0, 0.5, 2.5, -0.1]
for coeff, label in zip(coeffs, labels):
op = op + coeff * Choi(Operator.from_label(label))
target = np.sum(np.abs(coeffs))
try:
value = diamond_norm(op)
self.assertAlmostEqual(value, target, places=4)
except cvxpy.SolverError:
self.skipTest("CVXPY solver failed.")
def _fidelity_result(evals, evecs, target, qpt=False):
"""Faster computation of fidelity from eigen decomposition"""
# Format target to statevector or densitymatrix array
trace = np.sqrt(len(evals)) if qpt else 1
name = "process_fidelity" if qpt else "state_fidelity"
if target is None:
raise AnalysisError("No target state provided")
if isinstance(target, QuantumChannel):
target_state = Choi(target).data / trace
elif isinstance(target, BaseOperator):
target_state = np.ravel(Operator(target), order="F") / np.sqrt(trace)
else:
target_state = np.array(target)
if target_state.ndim == 1:
rho = evecs @ (evals / trace * evecs).T.conj()
fidelity = np.real(target_state.conj() @ rho @ target_state)
else:
sqrt_rho = evecs @ (np.sqrt(evals / trace) * evecs).T.conj()
eig = la.eigvalsh(sqrt_rho @ target_state @ sqrt_rho)
fidelity = np.sum(np.sqrt(np.maximum(eig, 0))) ** 2
return AnalysisResultData(name, fidelity)
def _run_analysis(self, experiment_data, **options):
# Extract tomography measurement data
outcome_data, shot_data, measurement_data, preparation_data = self._fitter_data(
experiment_data.data())
# Get tomography options
measurement_basis = options.pop("measurement_basis")
preparation_basis = options.pop("preparation_basis", None)
rescale_positive = options.pop("rescale_positive")
rescale_trace = options.pop("rescale_trace")
target_state = options.pop("target")
# Get target state from circuit metadata
if target_state == "default":
metadata = experiment_data.metadata
target_state = metadata.get("target", None)
# Get tomography fitter function
fitter = self._get_fitter(options.pop("fitter", None))
try:
t_fitter_start = time.time()
state, fitter_metadata = fitter(
outcome_data,
shot_data,
measurement_data,
preparation_data,
measurement_basis,
preparation_basis,
**options,
)
t_fitter_stop = time.time()
if fitter_metadata is None:
fitter_metadata = {}
state = Choi(state) if preparation_basis else DensityMatrix(state)
fitter_metadata["fitter"] = fitter.__name__
fitter_metadata["fitter_time"] = t_fitter_stop - t_fitter_start
analysis_results = self._postprocess_fit(
state,
metadata=fitter_metadata,
target_state=target_state,
rescale_positive=rescale_positive,
rescale_trace=rescale_trace,
qpt=bool(preparation_basis),
)
except AnalysisError as ex:
raise AnalysisError(
f"Tomography fitter failed with error: {str(ex)}") from ex
return analysis_results, []
def _state_result(
cls,
fit: np.ndarray,
make_positive: bool = False,
trace: Optional[float] = None,
input_dims: Optional[Tuple[int, ...]] = None,
output_dims: Optional[Tuple[int, ...]] = None,
) -> AnalysisResultData:
"""Convert fit data to state result data"""
# Get eigensystem of state fit
raw_eigvals, eigvecs = cls._state_eigensystem(fit)
# Optionally rescale eigenvalues to be non-negative
if make_positive and np.any(raw_eigvals < 0):
eigvals = cls._make_positive(raw_eigvals)
fit = eigvecs @ (eigvals * eigvecs).T.conj()
rescaled_psd = True
else:
eigvals = raw_eigvals
rescaled_psd = False
# Optionally rescale fit trace
fit_trace = np.sum(eigvals)
if trace is not None and not np.isclose(
fit_trace - trace, 0, atol=1e-12):
scale = trace / fit_trace
fit = fit * scale
eigvals = eigvals * scale
else:
trace = fit_trace
# Convert class of value
if input_dims and np.prod(input_dims) > 1:
value = Choi(fit, input_dims=input_dims, output_dims=output_dims)
else:
value = DensityMatrix(fit, dims=output_dims)
# Construct state result extra metadata
extra = {
"trace": trace,
"eigvals": eigvals,
"raw_eigvals": raw_eigvals,
"rescaled_psd": rescaled_psd,
"eigvecs": eigvecs,
}
return AnalysisResultData("state", value, extra=extra)
def _run_analysis(self, experiment_data):
# Extract tomography measurement data
outcome_data, shot_data, measurement_data, preparation_data = self._fitter_data(
experiment_data.data())
# Get tomography fitter function
fitter = self._get_fitter(self.options.fitter)
try:
t_fitter_start = time.time()
state, fitter_metadata = fitter(
outcome_data,
shot_data,
measurement_data,
preparation_data,
self.options.measurement_basis,
self.options.preparation_basis,
**self.options.fitter_options,
)
t_fitter_stop = time.time()
if fitter_metadata is None:
fitter_metadata = {}
state = Choi(
state) if self.options.preparation_basis else DensityMatrix(
state)
fitter_metadata["fitter"] = fitter.__name__
fitter_metadata["fitter_time"] = t_fitter_stop - t_fitter_start
analysis_results = self._postprocess_fit(
state,
metadata=fitter_metadata,
target_state=self.options.target,
rescale_positive=self.options.rescale_positive,
rescale_trace=self.options.rescale_trace,
qpt=bool(self.options.preparation_basis),
)
except AnalysisError as ex:
raise AnalysisError(
f"Tomography fitter failed with error: {str(ex)}") from ex
return analysis_results, []
def _split_input_vector(self, x: np.array) -> Tuple:
"""Reconstruct the GST data from its vector representation
Args:
x: The vector representation of the GST data
Returns:
The GST data (E, rho, Gs) (see additional info)
Additional information:
The gate set tomography data is a tuple (E, rho, Gs) consisting of
1) A POVM measurement operator E
2) An initial quantum state rho
3) A list Gs = (G1, G2, ..., Gk) of gates, represented as matrices
This function reconstructs (E, rho, Gs) from the vector x
Since the MLE optimization procedure has PSD constraints on
E, rho and the Choi represetnation of the PTM of the Gs,
we rely on the following property: M is PSD iff there exists
T such that M = T @ T^{dagger}.
Hence, x stores those T matrices for E, rho and the Gs
"""
n = len(self.Gs)
d = (2 ** self.qubits)
ds = d ** 2 # d squared - the dimension of the density operator
d_t = 2 * d ** 2
ds_t = 2 * ds ** 2
T_vars = self._split_list(x, [d_t, d_t] + [ds_t] * n)
E_T = self._vec_to_complex_matrix(T_vars[0])
rho_T = self._vec_to_complex_matrix(T_vars[1])
Gs_T = [self._vec_to_complex_matrix(T_vars[2+i]) for i in range(n)]
E = np.reshape(E_T @ np.conj(E_T.T), (1, ds))
rho = np.reshape(rho_T @ np.conj(rho_T.T), (ds, 1))
Gs = [PTM(Choi(G_T @ np.conj(G_T.T))).data for G_T in Gs_T]
return (E, rho, Gs)