qiskit-documentation/docs/api/qiskit/0.44/qiskit.algorithms.AmplitudeEstimation.mdx

---
title: AmplitudeEstimation
description: API reference for qiskit.algorithms.AmplitudeEstimation
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.algorithms.AmplitudeEstimation
---

# AmplitudeEstimation

<Class id="qiskit.algorithms.AmplitudeEstimation" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/algorithms/amplitude_estimators/ae.py" signature="qiskit.algorithms.AmplitudeEstimation(num_eval_qubits, phase_estimation_circuit=None, iqft=None, quantum_instance=None, sampler=None)" modifiers="class">
  Bases: [`AmplitudeEstimator`](qiskit.algorithms.AmplitudeEstimator "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.

  <Admonition title="Note" type="note">
    This class does not support the [`EstimationProblem.is_good_state`](qiskit.algorithms.EstimationProblem#is_good_state "qiskit.algorithms.EstimationProblem.is_good_state") property, as for phase estimation-based QAE, the oracle that identifes the good states must be encoded in the Grover operator. To set custom oracles, the [`EstimationProblem.grover_operator`](qiskit.algorithms.EstimationProblem#grover_operator "qiskit.algorithms.EstimationProblem.grover_operator") attribute can be set directly.
  </Admonition>

  **References**

  **\[1]: Brassard, G., Hoyer, P., Mosca, M., & Tapp, A. (2000).**

  Quantum Amplitude Amplification and Estimation. [arXiv:quant-ph/0005055](http://arxiv.org/abs/quant-ph/0005055).

  **\[2]: Grinko, D., Gacon, J., Zoufal, C., & Woerner, S. (2019).**

  Iterative Quantum Amplitude Estimation. [arXiv:1912.05559](https://arxiv.org/abs/1912.05559).

  <Admonition title="Deprecated since version 0.24.0" type="danger">
    `qiskit.algorithms.amplitude_estimators.ae.AmplitudeEstimation.__init__()`’s argument `quantum_instance` is deprecated as of qiskit-terra 0.24.0. It will be removed no earlier than 3 months after the release date. Instead, use the `sampler` argument. See [https://qisk.it/algo\_migration](https://qisk.it/algo_migration) for a migration guide.
  </Admonition>

  **Parameters**

  *   **num\_eval\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – The number of evaluation qubits.
  *   **phase\_estimation\_circuit** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *| None*) – 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** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *| None*) – The inverse quantum Fourier transform component, defaults to using a standard implementation from qiskit.circuit.library.QFT when None.
  *   **quantum\_instance** ([*QuantumInstance*](qiskit.utils.QuantumInstance "qiskit.utils.QuantumInstance")  *|*[*Backend*](qiskit.providers.Backend "qiskit.providers.Backend") *| None*) – Deprecated: The backend (or QuantumInstance) to execute the circuits on.
  *   **sampler** ([*BaseSampler*](qiskit.primitives.BaseSampler "qiskit.primitives.BaseSampler") *| None*) – A sampler primitive to evaluate the circuits.

  **Raises**

  [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError "(in Python v3.12)") – If the number of evaluation qubits is smaller than 1.

  ## Attributes

  ### quantum\_instance

  <Attribute id="qiskit.algorithms.AmplitudeEstimation.quantum_instance">
    Get the quantum instance.

    <Admonition title="Deprecated since version 0.24.0" type="danger">
      The property `qiskit.algorithms.amplitude_estimators.ae.AmplitudeEstimation.quantum_instance` is deprecated as of qiskit-terra 0.24.0. It will be removed no earlier than 3 months after the release date. See [https://qisk.it/algo\_migration](https://qisk.it/algo_migration) for a migration guide.
    </Admonition>

    **Returns**

    The quantum instance used to run this algorithm.

    **Type**

    Deprecated
  </Attribute>

  ### sampler

  <Attribute id="qiskit.algorithms.AmplitudeEstimation.sampler">
    Get the sampler primitive.

    **Returns**

    The sampler primitive to evaluate the circuits.
  </Attribute>

  ## Methods

  ### compute\_confidence\_interval

  <Function id="qiskit.algorithms.AmplitudeEstimation.compute_confidence_interval" signature="compute_confidence_interval(result, alpha=0.05, kind='likelihood_ratio')" modifiers="static">
    Compute the (1 - alpha) confidence interval.

    **Parameters**

    *   **result** ([*AmplitudeEstimationResult*](qiskit.algorithms.AmplitudeEstimationResult "qiskit.algorithms.amplitude_estimators.ae.AmplitudeEstimationResult")) – An amplitude estimation result for which to compute the confidence interval.
    *   **alpha** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")) – Confidence level: compute the (1 - alpha) confidence interval.
    *   **kind** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)")) – The method to compute the confidence interval, can be ‘fisher’, ‘observed\_fisher’ or ‘likelihood\_ratio’ (default)

    **Returns**

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

    **Raises**

    [**NotImplementedError**](https://docs.python.org/3/library/exceptions.html#NotImplementedError "(in Python v3.12)") – If the confidence interval method kind is not implemented.

    **Return type**

    [tuple](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.12)")\[[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)"), [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")]
  </Function>

  ### compute\_mle

  <Function id="qiskit.algorithms.AmplitudeEstimation.compute_mle" signature="compute_mle(result, apply_post_processing=False)" modifiers="static">
    Compute the Maximum Likelihood Estimator (MLE).

    **Parameters**

    *   **result** ([*AmplitudeEstimationResult*](qiskit.algorithms.AmplitudeEstimationResult "qiskit.algorithms.amplitude_estimators.ae.AmplitudeEstimationResult")) – An amplitude estimation result object.
    *   **apply\_post\_processing** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – If True, apply the post processing to the MLE before returning it.

    **Returns**

    The MLE for the provided result object.

    **Return type**

    [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")
  </Function>

  ### construct\_circuit

  <Function id="qiskit.algorithms.AmplitudeEstimation.construct_circuit" signature="construct_circuit(estimation_problem, measurement=False)">
    Construct the Amplitude Estimation quantum circuit.

    **Parameters**

    *   **estimation\_problem** ([*EstimationProblem*](qiskit.algorithms.EstimationProblem "qiskit.algorithms.amplitude_estimators.estimation_problem.EstimationProblem")) – The estimation problem for which to construct the QAE circuit.
    *   **measurement** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – Boolean flag to indicate if measurements should be included in the circuit.

    **Returns**

    The QuantumCircuit object for the constructed circuit.

    **Return type**

    [*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")
  </Function>

  ### estimate

  <Function id="qiskit.algorithms.AmplitudeEstimation.estimate" signature="estimate(estimation_problem)">
    Run the amplitude estimation algorithm on provided estimation problem.

    **Parameters**

    **estimation\_problem** ([*EstimationProblem*](qiskit.algorithms.EstimationProblem "qiskit.algorithms.amplitude_estimators.estimation_problem.EstimationProblem")) – The estimation problem.

    **Returns**

    An amplitude estimation results object.

    **Raises**

    *   [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError "(in Python v3.12)") – If state\_preparation or objective\_qubits are not set in the estimation\_problem.
    *   [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError "(in Python v3.12)") – A quantum instance or sampler must be provided.
    *   [**AlgorithmError**](algorithms#qiskit.algorithms.AlgorithmError "qiskit.algorithms.AlgorithmError") – Sampler job run error.

    **Return type**

    [*AmplitudeEstimationResult*](qiskit.algorithms.AmplitudeEstimationResult "qiskit.algorithms.amplitude_estimators.ae.AmplitudeEstimationResult")
  </Function>

  ### evaluate\_measurements

  <Function id="qiskit.algorithms.AmplitudeEstimation.evaluate_measurements" signature="evaluate_measurements(circuit_results, threshold=1e-06)">
    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** ([*dict*](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.12)")*\[*[*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)")*,* [*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")*] | np.ndarray*) – The circuit result from the QAE circuit. Can be either a counts dict or a statevector or a quasi-probabilities dict.
    *   **threshold** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")) – Measurements with probabilities below the threshold are discarded.

    **Returns**

    **Dictionaries containing the a gridpoints with respective probabilities and**

    y measurements with respective probabilities, in this order.

    **Return type**

    [tuple](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.12)")\[[dict](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.12)")\[[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)"), [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")], [dict](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.12)")\[[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)"), [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")]]
  </Function>
</Class>