---
title: FasterAmplitudeEstimation (v0.46)
description: API reference for qiskit.algorithms.FasterAmplitudeEstimation in qiskit v0.46
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/0.46/qiskit.algorithms.FasterAmplitudeEstimation
---

# FasterAmplitudeEstimation

*class* `qiskit.algorithms.FasterAmplitudeEstimation(delta, maxiter, rescale=True, quantum_instance=None, sampler=None)`

[GitHub](https://github.com/qiskit/qiskit/tree/stable/0.46/qiskit/algorithms/amplitude_estimators/fae.py)

Bases: [`AmplitudeEstimator`](/docs/api/qiskit/0.46/qiskit.algorithms.AmplitudeEstimator "qiskit.algorithms.amplitude_estimators.amplitude_estimator.AmplitudeEstimator")

The Faster Amplitude Estimation algorithm.

The Faster Amplitude Estimation (FAE) \[1] algorithm is a variant of Quantum Amplitude Estimation (QAE), where the Quantum Phase Estimation (QPE) by an iterative Grover search, similar to \[2].

Due to the iterative version of the QPE, this algorithm does not require any additional qubits, as the originally proposed QAE \[3] and thus the resulting circuits are less complex.

**References**

**\[1]: K. Nakaji. Faster Amplitude Estimation, 2020;**

[arXiv:2002.02417](https://arxiv.org/pdf/2003.02417.pdf)

**\[2]: D. Grinko et al. Iterative Amplitude Estimation, 2019;**

[arXiv:1912.05559](http://arxiv.org/abs/1912.05559)

**\[3]: G. Brassard et al. Quantum Amplitude Amplification and Estimation, 2000;**

[arXiv:quant-ph/0005055](http://arxiv.org/abs/quant-ph/0005055)

> **Deprecated since version 0.24.0**
>
> `qiskit.algorithms.amplitude_estimators.fae.FasterAmplitudeEstimation.__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.

**Parameters**

- **delta** ([*float*](https://docs.python.org/3/library/functions.html#float)) – The probability that the true value is outside of the final confidence interval.
- **maxiter** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of iterations, the maximal power of Q is 2 \*\* (maxiter - 1).
- **rescale** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to rescale the problem passed to estimate.
- **quantum\_instance** ([*QuantumInstance*](/docs/api/qiskit/0.46/qiskit.utils.QuantumInstance "qiskit.utils.QuantumInstance")  *|*[*Backend*](/docs/api/qiskit/0.46/qiskit.providers.Backend "qiskit.providers.Backend") *| None*) – Deprecated: The quantum instance or backend to run the circuits.
- **sampler** ([*BaseSampler*](/docs/api/qiskit/0.46/qiskit.primitives.BaseSampler "qiskit.primitives.BaseSampler") *| None*) – A sampler primitive to evaluate the circuits.

> **Note**
>
> This algorithm overwrites the number of shots set in the `quantum_instance` argument, but will reset them to the initial number after running.

## Attributes

### quantum\_instance

Deprecated. Get the quantum instance.

> **Deprecated since version 0.24.0**
>
> The property `qiskit.algorithms.amplitude_estimators.fae.FasterAmplitudeEstimation.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.

**Returns**

The quantum instance used to run this algorithm.

### sampler

Get the sampler primitive.

**Returns**

The sampler primitive to evaluate the circuits.

## Methods

### construct\_circuit

`construct_circuit(estimation_problem, k, measurement=False)`

Construct the circuit $Q^k X |0\rangle>$.

The A operator is the unitary specifying the QAE problem and Q the associated Grover operator.

**Parameters**

- **estimation\_problem** ([*EstimationProblem*](/docs/api/qiskit/0.46/qiskit.algorithms.EstimationProblem "qiskit.algorithms.EstimationProblem")) – The estimation problem for which to construct the circuit.
- **k** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The power of the Q operator.
- **measurement** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Boolean flag to indicate if measurements should be included in the circuits.

**Returns**

The circuit $Q^k X |0\rangle$.

**Return type**

[QuantumCircuit](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") | [tuple](https://docs.python.org/3/library/stdtypes.html#tuple)\[[QuantumCircuit](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit"), [list](https://docs.python.org/3/library/stdtypes.html#list)\[[int](https://docs.python.org/3/library/functions.html#int)]]

### estimate

`estimate(estimation_problem)`

Run the amplitude estimation algorithm on provided estimation problem.

**Parameters**

**estimation\_problem** ([*EstimationProblem*](/docs/api/qiskit/0.46/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) – A quantum instance or Sampler must be provided.
- [**AlgorithmError**](/docs/api/qiskit/0.46/algorithms#qiskit.algorithms.AlgorithmError "qiskit.algorithms.AlgorithmError") – Sampler run error.

**Return type**

[*FasterAmplitudeEstimationResult*](/docs/api/qiskit/0.46/qiskit.algorithms.FasterAmplitudeEstimationResult "qiskit.algorithms.amplitude_estimators.fae.FasterAmplitudeEstimationResult")