MaximumLikelihoodAmplitudeEstimation

class MaximumLikelihoodAmplitudeEstimation(evaluation_schedule, minimizer=None, quantum_instance=None)

Bases: qiskit.algorithms.amplitude_estimators.amplitude_estimator.AmplitudeEstimator

The Maximum Likelihood Amplitude Estimation algorithm.

This class implements the quantum amplitude estimation (QAE) algorithm without phase estimation, as introduced in [1]. In comparison to the original QAE algorithm [2], this implementation relies solely on different powers of the Grover operator and does not require additional evaluation qubits. Finally, the estimate is determined via a maximum likelihood estimation, which is why this class in named MaximumLikelihoodAmplitudeEstimation.

References

[1]: Suzuki, Y., Uno, S., Raymond, R., Tanaka, T., Onodera, T., & Yamamoto, N. (2019).

Amplitude Estimation without Phase Estimation. arXiv:1904.10246.

[2]: Brassard, G., Hoyer, P., Mosca, M., & Tapp, A. (2000).

Quantum Amplitude Amplification and Estimation. arXiv:quant-ph/0005055.

Parameters

• evaluation_schedule (Union[List[int], int]) – If a list, the powers applied to the Grover operator. The list element must be non-negative. If a non-negative integer, an exponential schedule is used where the highest power is 2 to the integer minus 1: [id, Q^2^0, …, Q^2^(evaluation_schedule-1)].

• minimizer (Optional[Callable[[Callable[[float], float], List[Tuple[float, float]]], float]]) – A minimizer used to find the minimum of the likelihood function. Defaults to a brute search where the number of evaluation points is determined according to evaluation_schedule. The minimizer takes a function as first argument and a list of (float, float) tuples (as bounds) as second argument and returns a single float which is the found minimum.

• quantum_instance (Union[Backend, BaseBackend, QuantumInstance, None]) – Quantum Instance or Backend

Raises

ValueError – If the number of oracle circuits is smaller than 1.

Methods

compute_confidence_interval	Compute the alpha confidence interval using the method kind.
compute_mle	Compute the MLE via a grid-search.
construct_circuits	Construct the Amplitude Estimation w/o QPE quantum circuits.
estimate	Run the amplitude estimation algorithm.

Attributes

quantum_instance

Get the quantum instance.

Return type

Optional[QuantumInstance]

Returns

The quantum instance used to run this algorithm.