qiskit.algorithms.AmplitudeEstimation¶

class AmplitudeEstimation(num_eval_qubits, phase_estimation_circuit=None, iqft=None, quantum_instance=None)[source]¶

The Quantum Phase Estimation-based Amplitude Estimation algorithm.

This class implements the original Quantum Amplitude Estimation (QAE) algorithm, introduced by [1]. This canonical version uses quantum phase estimation along with a set of \(m\) additional evaluation qubits to find an estimate \(\tilde{a}\), that is restricted to the grid

\[\tilde{a} \in \{\sin^2(\pi y / 2^m) : y = 0, ..., 2^{m-1}\}\]

More evaluation qubits produce a finer sampling grid, therefore the accuracy of the algorithm increases with \(m\).

Using a maximum likelihood post processing, this grid constraint can be circumvented. This improved estimator is implemented as well, see [2] Appendix A for more detail.

References

[1]: Brassard, G., Hoyer, P., Mosca, M., & Tapp, A. (2000).: Quantum Amplitude Amplification and Estimation. arXiv:quant-ph/0005055.
[2]: Grinko, D., Gacon, J., Zoufal, C., & Woerner, S. (2019).: Iterative Quantum Amplitude Estimation. arXiv:1912.05559.

Parameters

num_eval_qubits (int) – The number of evaluation qubits.
phase_estimation_circuit (Optional[QuantumCircuit]) – The phase estimation circuit used to run the algorithm. Defaults to the standard phase estimation circuit from the circuit library, qiskit.circuit.library.PhaseEstimation when None.
iqft (Optional[QuantumCircuit]) – The inverse quantum Fourier transform component, defaults to using a standard implementation from qiskit.circuit.library.QFT when None.
quantum_instance (Union[Backend, BaseBackend, QuantumInstance, None]) – The backend (or QuantumInstance) to execute the circuits on.

Raises

ValueError – If the number of evaluation qubits is smaller than 1.

__init__(num_eval_qubits, phase_estimation_circuit=None, iqft=None, quantum_instance=None)[source]¶

Parameters

num_eval_qubits (int) – The number of evaluation qubits.
phase_estimation_circuit (Optional[QuantumCircuit]) – The phase estimation circuit used to run the algorithm. Defaults to the standard phase estimation circuit from the circuit library, qiskit.circuit.library.PhaseEstimation when None.
iqft (Optional[QuantumCircuit]) – The inverse quantum Fourier transform component, defaults to using a standard implementation from qiskit.circuit.library.QFT when None.
quantum_instance (Union[Backend, BaseBackend, QuantumInstance, None]) – The backend (or QuantumInstance) to execute the circuits on.

Raises

ValueError – If the number of evaluation qubits is smaller than 1.

Methods

`__init__`(num_eval_qubits[, …])	type num_eval_qubits `int`
`compute_confidence_interval`(result[, alpha, …])	Compute the (1 - alpha) confidence interval.
`compute_mle`(result[, apply_post_processing])	Compute the Maximum Likelihood Estimator (MLE).
`construct_circuit`(estimation_problem[, …])	Construct the Amplitude Estimation quantum circuit.
`estimate`(estimation_problem)	Run the amplitude estimation algorithm on provided estimation problem.
`evaluate_measurements`(circuit_results[, …])	Evaluate the results from the circuit simulation.

Attributes

quantum_instance

Get the quantum instance.

static compute_confidence_interval(result, alpha=0.05, kind='likelihood_ratio')[source]¶

Compute the (1 - alpha) confidence interval.

Parameters

result (AmplitudeEstimationResult) – An amplitude estimation result for which to compute the confidence interval.
alpha (float) – Confidence level: compute the (1 - alpha) confidence interval.
kind (str) – The method to compute the confidence interval, can be ‘fisher’, ‘observed_fisher’ or ‘likelihood_ratio’ (default)

Return type

Tuple[float, float]

Returns

The (1 - alpha) confidence interval of the specified kind.

Raises

AquaError – If ‘mle’ is not in self._ret.keys() (i.e. run was not called yet).
NotImplementedError – If the confidence interval method kind is not implemented.

static compute_mle(result, apply_post_processing=False)[source]¶

Compute the Maximum Likelihood Estimator (MLE).

Parameters

result (AmplitudeEstimationResult) – An amplitude estimation result object.
apply_post_processing (bool) – If True, apply the post processing to the MLE before returning it.

Return type

float

Returns

The MLE for the provided result object.

construct_circuit(estimation_problem, measurement=False)[source]¶

Construct the Amplitude Estimation quantum circuit.

Parameters

estimation_problem (EstimationProblem) – The estimation problem for which to construct the QAE circuit.
measurement (bool) – Boolean flag to indicate if measurements should be included in the circuit.

Return type

QuantumCircuit

Returns

The QuantumCircuit object for the constructed circuit.

estimate(estimation_problem)[source]¶

Run the amplitude estimation algorithm on provided estimation problem.

Parameters: estimation_problem (EstimationProblem) – The estimation problem.
Return type: AmplitudeEstimationResult
Returns: An amplitude estimation results object.
Raises: ValueError – If state_preparation or objective_qubits are not set in the estimation_problem.

evaluate_measurements(circuit_results, threshold=1e-06)[source]¶

Evaluate the results from the circuit simulation.

Given the probabilities from statevector simulation of the QAE circuit, compute the probabilities that the measurements y/gridpoints a are the best estimate.

Parameters

circuit_results (Union[Dict[str, int], ndarray]) – The circuit result from the QAE circuit. Can be either a counts dict or a statevector.
threshold (float) – Measurements with probabilities below the threshold are discarded.

Return type

Tuple[Dict[int, float], Dict[float, float]]

Returns

Dictionaries containing the a gridpoints with respective probabilities and: y measurements with respective probabilities, in this order.

property quantum_instance¶

Get the quantum instance.

Return type: Optional[QuantumInstance]
Returns: The quantum instance used to run this algorithm.