---
title: unitary_overlap (latest version)
description: API reference for qiskit.circuit.library.unitary_overlap in the latest version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.unitary_overlap
---

# qiskit.circuit.library.unitary\_overlap

`qiskit.circuit.library.unitary_overlap(unitary1, unitary2, prefix1='p1', prefix2='p2', insert_barrier=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/overlap.py#L105-L183)

Circuit that returns the overlap between two unitaries $U_2^{\dag} U_1$.

The input quantum circuits must represent unitary operations, since they must be invertible. If the inputs will have parameters, they are replaced by [`ParameterVector`](/docs/api/qiskit/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector")s with names “p1” (for circuit `unitary1`) and “p2” (for circuit `unitary_2`) in the output circuit.

This circuit is usually employed in computing the fidelity:

$$
\left|\langle 0| U_2^{\dag} U_1|0\rangle\right|^{2}
$$

by computing the probability of being in the all-zeros bit-string, or equivalently, the expectation value of projector $|0\rangle\langle 0|$.

Reference Circuit:

```python
import numpy as np
from qiskit.circuit.library import efficient_su2, unitary_overlap

# get two circuit to prepare states of which we compute the overlap
circuit = efficient_su2(2, reps=1)
unitary1 = circuit.assign_parameters(np.random.random(circuit.num_parameters))
unitary2 = circuit.assign_parameters(np.random.random(circuit.num_parameters))

# create the overlap circuit
overlap = unitary_overlap(unitary1, unitary2)
overlap.draw('mpl')
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/qiskit-circuit-library-unitary_overlap-1.avif)

**Parameters**

- **unitary1** ([*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")) – Unitary acting on the ket vector.
- **unitary2** ([*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")) – Unitary whose inverse operates on the bra vector.
- **prefix1** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the parameter vector associated to `unitary1`, if it is parameterized. Defaults to `"p1"`.
- **prefix2** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the parameter vector associated to `unitary2`, if it is parameterized. Defaults to `"p2"`.
- **insert\_barrier** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to insert a barrier between the two unitaries.

**Raises**

- [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – Number of qubits in `unitary1` and `unitary2` does not match.
- [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – Inputs contain measurements and/or resets.

**Return type**

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