AmplitudeEstimation¶

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

Bases: qiskit.algorithms.amplitude_estimators.amplitude_estimator.AmplitudeEstimator

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.

Methods

`compute_confidence_interval`	Compute the (1 - alpha) confidence interval.
`compute_mle`	Compute the Maximum Likelihood Estimator (MLE).
`construct_circuit`	Construct the Amplitude Estimation quantum circuit.
`estimate`	Run the amplitude estimation algorithm on provided estimation problem.
`evaluate_measurements`	Evaluate the results from the circuit simulation.

Attributes

quantum_instance¶

Get the quantum instance.

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