---
title: phase_estimation (v2.4)
description: API reference for qiskit.circuit.library.phase_estimation in qiskit v2.4
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.4/qiskit.circuit.library.phase_estimation
---

# qiskit.circuit.library.phase\_estimation

`qiskit.circuit.library.phase_estimation(num_evaluation_qubits, unitary, name='QPE')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/circuit/library/phase_estimation.py#L111-L184)

Phase Estimation circuit.

In the Quantum Phase Estimation (QPE) algorithm \[1, 2, 3], the Phase Estimation circuit is used to estimate the phase $\phi$ of an eigenvalue $e^{2\pi i\phi}$ of a unitary operator $U$, provided with the corresponding eigenstate $|\psi\rangle$. That is

$$
U|\psi\rangle = e^{2\pi i\phi} |\psi\rangle
$$

This estimation (and thereby this circuit) is a central routine to several well-known algorithms, such as Shor’s algorithm or Quantum Amplitude Estimation.

**Parameters**

- **num\_evaluation\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of evaluation qubits.
- **unitary** ([*QuantumCircuit*](/docs/api/qiskit/2.4/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")  *|*[*Gate*](/docs/api/qiskit/2.4/qiskit.circuit.Gate "qiskit.circuit.gate.Gate")) – The unitary operation $U$ which will be repeated and controlled. This can either be a [`QuantumCircuit`](/docs/api/qiskit/2.4/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") or a [`Gate`](/docs/api/qiskit/2.4/qiskit.circuit.Gate "qiskit.circuit.Gate"). Passing gates can often be more performant, as it allows calling optimized control and power subroutines.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the output circuit.

**Return type**

[*QuantumCircuit*](/docs/api/qiskit/2.4/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

Reference Circuit:

```python
from qiskit.circuit.library import phase_estimation, PauliEvolutionGate
from qiskit.quantum_info import SparsePauliOp

hamiltonian = SparsePauliOp(["ZZ", "IX", "XI"])
evo = PauliEvolutionGate(hamiltonian, time=0.1)  # implements exp(-itH)

circuit = phase_estimation(3, evo)  # QPE for the evolution operator
circuit.draw("mpl")
```

![A phase estimation circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.4/qiskit-circuit-library-phase_estimation-1.avif)

References:

\[1] Kitaev, A. Y. (1995). Quantum measurements and the Abelian Stabilizer Problem. 1–22. [quant-ph/9511026](https://arxiv.org/abs/quant-ph/9511026)

\[2] Michael A. Nielsen and Isaac L. Chuang. 2011. Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.). Cambridge University Press, New York, NY, USA.

\[3] Qiskit [textbook](https://github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/quantum-phase-estimation.ipynb)