> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Unitary Function

<Card title="View on GitHub" icon="github" href="https://github.com/Classiq/classiq-library/blob/main/functions/qmod_library_reference/qmod_core_library/unitary/unitary.ipynb">
  Open this notebook in GitHub to run it yourself
</Card>

Given a $2^{n}\times2^{n}$ unitary matrix, the unitary-gate function constructs an
equivalent unitary function that acts on $n$ qubits accordingly.

For $n>2$, the
synthesis process implementation is based on [\[1\]](#1).

Function: `unitary`

Arguments:

* `elements: CArray[CArray[CReal]]`

* A 2d array of complex numbers representing the unitary matrix.

* `target: QArray[QBit]`

* The quantum state to apply the unitary on.

Should be of corresponding size.

## Example

This example shows a $2$-qubit unitary function application in the formed $4$-dimensional space.

```python theme={null}
from classiq import *

UNITARY = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1j, 0], [0, 0, 0, 1j]]


@qfunc
def main(x: Output[QArray[QBit]]):
    allocate(2, x)
    unitary(UNITARY, x)


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)
```

## References

<a name="1">\[1]</a> R. Iten et al, Quantum Circuits for Isometries, Phys. Rev. A 93 (2016). [https://link.aps.org/doi/10.1103/PhysRevA.93.032318](https://link.aps.org/doi/10.1103/PhysRevA.93.032318)