CTMPExpvalMeasMitigator

CTMPExpvalMeasMitigator.assignment_fidelity(qubits=None)

Return the measurement assignment fidelity on the specified qubits.

The assignment fidelity on N-qubits is defined as $\sum_{x\in\{0, 1\}^n} P(x|x) / 2^n$, where $P(x|x) = \rangle x|A|x\langle$, and $A$ is the assignment_matrix().

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the assignment fidelity.

Return type

float

CTMPExpvalMeasMitigator.assignment_matrix(qubits=None)

Return the measurement assignment matrix for specified qubits.

The assignment matrix is the stochastic matrix $A$ which assigns a noisy measurement probability distribution to an ideal input measurement distribution: $P(i|j) = \langle i | A | j \rangle$.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the assignment matrix A.

Return type

np.ndarray

CTMPExpvalMeasMitigator.expectation_value(counts, diagonal=None, qubits=None, clbits=None)

Compute the mitigated expectation value of a diagonal observable.

This computes the mitigated estimator of $\langle O \rangle = \text{Tr}[\rho. O]$ of a diagonal observable $O = \sum_{x\in\{0, 1\}^n} O(x)|x\rangle\!\langle x|$.

Parameters

• counts (Dict) – counts object
• diagonal (Optional[ndarray]) – Optional, the vector of diagonal values for summing the expectation value. If None the the default value is $[1, -1]^\otimes n$.
• qubits (Optional[List[int]]) – Optional, the measured physical qubits the count bitstrings correspond to. If None qubits are assumed to be $[0, ..., n-1]$.
• clbits (Optional[List[int]]) – Optional, if not None marginalize counts to the specified bits.

Returns

the expectation value and standard deviation.

Return type

(float, float)

Additional Information:

The diagonal observable $O$ is input using the diagonal kwarg as a list or Numpy array $[O(0), ..., O(2^n -1)]$. 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).

CTMPExpvalMeasMitigator.generator_matrix(qubits=None)

Return the generator matrix on the specified qubits.

The generator matrix $G$ is given by $\sum_i r_i G_i$ where the sum is taken over all $G_i$ acting on the specified qubits subset.

Parameters

qubits (Optional[List[int]]) – Optional, qubit subset for the generators.

Returns

the generator matrix $G$.

Return type

sps.coo_matrix

CTMPExpvalMeasMitigator.mitigation_matrix(qubits=None)

Return the measurement mitigation matrix for the specified qubits.

The mitigation matrix $A^{-1}$ is defined as the inverse of the assignment_matrix() $A$.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the measurement error mitigation matrix $A^{-1}$.

Return type

np.ndarray

CTMPExpvalMeasMitigator.mitigation_overhead(qubits=None)

Return the mitigation overhead for expectation value estimation.

This is the multiplicative factor of extra shots required for estimating a mitigated expectation value with the same accuracy as an unmitigated expectation value.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the mitigation overhead factor.

Return type

int

CTMPExpvalMeasMitigator.noise_strength(qubits=None)

Return the noise strength $gamma$ on the specified qubits

Return type

float

CTMPExpvalMeasMitigator.plot_assignment_matrix(qubits=None, ax=None)

Matrix plot of the readout error assignment matrix.

Parameters

• qubits (list(int)) – Optional, qubits being measured for operator expval.
• ax (axes) – Optional. Axes object to add plot to.

Returns

the figure axes object.

Return type

plt.axes

Raises

ImportError – if matplotlib is not installed.

CTMPExpvalMeasMitigator.plot_mitigation_matrix(qubits=None, ax=None)

Matrix plot of the readout error mitigation matrix.

Parameters

• qubits (list(int)) – Optional, qubits being measured for operator expval.
• ax (plt.axes) – Optional. Axes object to add plot to.

Returns

the figure axes object.

Return type

plt.axes

Raises

ImportError – if matplotlib is not installed.

CTMPExpvalMeasMitigator.required_shots(delta, qubits=None)

Return the number of shots required for expectation value estimation.

This is the number of shots required so that $|\langle O \rangle_{est} - \langle O \rangle_{true}| < \delta$ with high probability (at least 2/3) and is given by $4\delta^2 \Gamma^2$ where $\Gamma^2$ is the mitigation_overhead().

Parameters

• delta (float) – Error tolerance for expectation value estimator.
• qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the required shots.

Return type

int

CTMPExpvalMeasMitigator.seed(value=None)

Set the seed for the quantum state RNG.

CTMPExpvalMeasMitigator.stddev_upper_bound(shots=1, qubits=None)

Return an upper bound on standard deviation of expval estimator.

Parameters

• shots (int) – Number of shots used for expectation value measurement.
• qubits (Optional[List[int]]) – qubits being measured for operator expval.

Returns

the standard deviation upper bound.

Return type

float