"""1-qubit tensor product readout error mitigator.

Mitigates :meth:`expectation_value` and :meth:`quasi_probabilities`.

The mitigator should either be calibrated using qiskit experiments,

or calculated directly from the backend properties.

This mitigation method should be used in case the readout errors of the qubits

are assumed to be uncorrelated. For *N* qubits there are *N* mitigation matrices,

each of size :math:`2 x 2` and the mitigation complexity is :math:`O(2^N)`,

so it is more efficient than the :class:`CorrelatedReadoutMitigator` class.

"""

def __init__(

self,

assignment_matrices: Optional[List[np.ndarray]] = None,

qubits: Optional[Iterable[int]] = None,

backend=None,

):

"""Initialize a LocalReadoutMitigator

Args:

assignment_matrices: Optional, list of single-qubit readout error assignment matrices.

qubits: Optional, the measured physical qubits for mitigation.

backend: Optional, backend name.

Raises:

QiskitError: matrices sizes do not agree with number of qubits

"""

if assignment_matrices is None:

assignment_matrices = self._from_backend(backend, qubits)

else:

assignment_matrices = [np.asarray(amat, dtype=float) for amat in assignment_matrices]

for amat in assignment_matrices:

if np.any(amat < 0) or not np.allclose(np.sum(amat, axis=0), 1):

raise QiskitError(

"Assignment matrix columns must be valid probability distributions"

)

if qubits is None:

self._num_qubits = len(assignment_matrices)

self._qubits = range(self._num_qubits)

else:

if len(qubits) != len(assignment_matrices):

raise QiskitError(

"The number of given qubits ({}) is different than the number of qubits "

"inferred from the matrices ({})".format(len(qubits), len(assignment_matrices))

)

self._qubits = qubits

self._num_qubits = len(self._qubits)

self._qubit_index = dict(zip(self._qubits, range(self._num_qubits)))

self._assignment_mats = assignment_matrices

self._mitigation_mats = np.zeros([self._num_qubits, 2, 2], dtype=float)

self._gammas = np.zeros(self._num_qubits, dtype=float)

for i in range(self._num_qubits):

mat = self._assignment_mats[i]

# Compute Gamma values

error0 = mat[1, 0]

error1 = mat[0, 1]

self._gammas[i] = (1 + abs(error0 - error1)) / (1 - error0 - error1)

# Compute inverse mitigation matrix

try:

ainv = np.linalg.inv(mat)

except np.linalg.LinAlgError:

ainv = np.linalg.pinv(mat)

self._mitigation_mats[i] = ainv

@property

def settings(self) -> Dict:

"""Return settings."""

return {"assignment_matrices": self._assignment_mats, "qubits": self._qubits}

def expectation_value(

self,

data: Counts,

diagonal: Union[Callable, dict, str, np.ndarray] = None,

qubits: Iterable[int] = None,

clbits: Optional[List[int]] = None,

shots: Optional[int] = None,

) -> Tuple[float, float]:

r"""Compute the mitigated expectation value of a diagonal observable.

This computes the mitigated estimator of

:math:`\langle O \rangle = \mbox{Tr}[\rho. O]` of a diagonal observable

:math:`O = \sum_{x\in\{0, 1\}^n} O(x)|x\rangle\!\langle x|`.

Args:

data: Counts object

diagonal: Optional, the vector of diagonal values for summing the

expectation value. If ``None`` the default value is

:math:`[1, -1]^\otimes n`.

qubits: Optional, the measured physical qubits the count

bitstrings correspond to. If None qubits are assumed to be

:math:`[0, ..., n-1]`.

clbits: Optional, if not None marginalize counts to the specified bits.

shots: the number of shots.

Returns:

(float, float): the expectation value and an upper bound of the standard deviation.

Additional Information:

The diagonal observable :math:`O` is input using the ``diagonal`` kwarg as

a list or Numpy array :math:`[O(0), ..., O(2^n -1)]`. If no diagonal is specified

the diagonal of the Pauli operator

:math`O = \mbox{diag}(Z^{\otimes n}) = [1, -1]^{\otimes n}` is used.

The ``clbits`` kwarg is used to marginalize the input counts dictionary

over the specified bit-values, and the ``qubits`` kwarg is used to specify

which physical qubits these bit-values correspond to as

``circuit.measure(qubits, clbits)``.

"""

if qubits is None:

qubits = self._qubits

num_qubits = len(qubits)

probs_vec, shots = counts_probability_vector(

data, qubit_index=self._qubit_index, clbits=clbits, qubits=qubits

)

# Get qubit mitigation matrix and mitigate probs

qubit_indices = [self._qubit_index[qubit] for qubit in qubits]

ainvs = self._mitigation_mats[qubit_indices]

# Get operator coeffs

if diagonal is None:

diagonal = z_diagonal(2**num_qubits)

elif isinstance(diagonal, str):

diagonal = str2diag(diagonal)

# Apply transpose of mitigation matrix

coeffs = np.reshape(diagonal, num_qubits * [2])

einsum_args = [coeffs, list(range(num_qubits))]

for i, ainv in enumerate(reversed(ainvs)):

einsum_args += [ainv.T, [num_qubits + i, i]]

einsum_args += [list(range(num_qubits, 2 * num_qubits))]

coeffs = np.einsum(*einsum_args).ravel()

expval = coeffs.dot(probs_vec)

stddev_upper_bound = self.stddev_upper_bound(shots, qubits)

return (expval, stddev_upper_bound)

def quasi_probabilities(

self,

data: Counts,

qubits: Optional[List[int]] = None,

clbits: Optional[List[int]] = None,

shots: Optional[int] = None,

) -> QuasiDistribution:

"""Compute mitigated quasi probabilities value.

Args:

data: counts object

qubits: qubits the count bitstrings correspond to.

clbits: Optional, marginalize counts to just these bits.

shots: Optional, the total number of shots, if None shots will

be calculated as the sum of all counts.

Returns:

QuasiDistribution: A dictionary containing pairs of [output, mean] where "output"

is the key in the dictionaries,

which is the length-N bitstring of a measured standard basis state,

and "mean" is the mean of non-zero quasi-probability estimates.

Raises:

QiskitError: if qubit and clbit kwargs are not valid.

"""

if qubits is None:

qubits = self._qubits

num_qubits = len(qubits)

probs_vec, calculated_shots = counts_probability_vector(

data, qubit_index=self._qubit_index, clbits=clbits, qubits=qubits

)

if shots is None:

shots = calculated_shots

# Get qubit mitigation matrix and mitigate probs

qubit_indices = [self._qubit_index[qubit] for qubit in qubits]

ainvs = self._mitigation_mats[qubit_indices]

# Apply transpose of mitigation matrix

prob_tens = np.reshape(probs_vec, num_qubits * [2])

einsum_args = [prob_tens, list(range(num_qubits))]

for i, ainv in enumerate(reversed(ainvs)):

einsum_args += [ainv, [num_qubits + i, i]]

einsum_args += [list(range(num_qubits, 2 * num_qubits))]

probs_vec = np.einsum(*einsum_args).ravel()

probs_dict = {}

for index, _ in enumerate(probs_vec):

probs_dict[index] = probs_vec[index]

quasi_dist = QuasiDistribution(

probs_dict, shots=shots, stddev_upper_bound=self.stddev_upper_bound(shots, qubits)

)

return quasi_dist

def mitigation_matrix(self, qubits: Optional[Union[List[int], int]] = None) -> np.ndarray:

r"""Return the measurement mitigation matrix for the specified qubits.

The mitigation matrix :math:`A^{-1}` is defined as the inverse of the

:meth:`assignment_matrix` :math:`A`.

Args:

qubits: Optional, qubits being measured for operator expval.

if a single int is given, it is assumed to be the index

of the qubit in self._qubits

Returns:

np.ndarray: the measurement error mitigation matrix :math:`A^{-1}`.

"""

if qubits is None:

qubits = self._qubits

if isinstance(qubits, int):

qubits = [self._qubits[qubits]]

qubit_indices = [self._qubit_index[qubit] for qubit in qubits]

mat = self._mitigation_mats[qubit_indices[0]]

for i in qubit_indices[1:]:

mat = np.kron(self._mitigation_mats[i], mat)

return mat

def assignment_matrix(self, qubits: List[int] = None) -> np.ndarray:

r"""Return the measurement assignment matrix for specified qubits.

The assignment matrix is the stochastic matrix :math:`A` which assigns

a noisy measurement probability distribution to an ideal input

measurement distribution: :math:`P(i|j) = \langle i | A | j \rangle`.

Args:

qubits: Optional, qubits being measured for operator expval.

Returns:

np.ndarray: the assignment matrix A.

"""

if qubits is None:

qubits = self._qubits

if isinstance(qubits, int):

qubits = [qubits]

qubit_indices = [self._qubit_index[qubit] for qubit in qubits]

mat = self._assignment_mats[qubit_indices[0]]

for i in qubit_indices[1:]:

mat = np.kron(self._assignment_mats[i], mat)

return mat

def _compute_gamma(self, qubits=None):

"""Compute gamma for N-qubit mitigation"""

if qubits is None:

gammas = self._gammas

else:

qubit_indices = [self._qubit_index[qubit] for qubit in qubits]

gammas = self._gammas[qubit_indices]

return np.prod(gammas)

def stddev_upper_bound(self, shots: int, qubits: List[int] = None):

"""Return an upper bound on standard deviation of expval estimator.

Args:

shots: Number of shots used for expectation value measurement.

qubits: qubits being measured for operator expval.

Returns:

float: the standard deviation upper bound.

"""

gamma = self._compute_gamma(qubits=qubits)

return gamma / math.sqrt(shots)

def _from_backend(self, backend, qubits):

"""Calculates amats from backend properties readout_error"""

backend_qubits = backend.properties().qubits

if qubits is not None:

if any(qubit >= len(backend_qubits) for qubit in qubits):

raise QiskitError("The chosen backend does not contain the specified qubits.")

reduced_backend_qubits = [backend_qubits[i] for i in qubits]

backend_qubits = reduced_backend_qubits

num_qubits = len(backend_qubits)

amats = np.zeros([num_qubits, 2, 2], dtype=float)

for qubit_idx, qubit_prop in enumerate(backend_qubits):

for prop in qubit_prop:

if prop.name == "prob_meas0_prep1":

(amats[qubit_idx])[0, 1] = prop.value

(amats[qubit_idx])[1, 1] = 1 - prop.value

if prop.name == "prob_meas1_prep0":

(amats[qubit_idx])[1, 0] = prop.value

(amats[qubit_idx])[0, 0] = 1 - prop.value

return amats

@property

def qubits(self) -> Tuple[int]:

"""The device qubits for this mitigator"""