> ## 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.

# Multi-Control-X

<Card title="View on GitHub" icon="github" href="https://github.com/Classiq/classiq-library/blob/main/functions/function_usage_examples/mcx/mcx_example.ipynb">
  Open this notebook in GitHub to run it yourself
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The multi-control-X applies X gate to one target qubit bit only if the logical AND of all control qubits is satisfied.

The multi-control-X function incorporates numerous implementations for the multi-control-X gate,
each with a different depth and number of auxiliary qubits.

These implementations generically outperform the Gray-code, V-chain and recursive implementations of Ref. [\[1\]](#1),
as well as the relative-phase Toffoli implementation of Ref. [\[2\]](#2).

Given a sufficient number of auxiliary qubits, some implementations allow for logarithmic depth and linear CX-count.

The synthesis process selects the appropriate implementation depending on the defined constraints.

Operator: `control`

Arguments:

* `ctrl: Union[QBit, QArray[QBit]]`
* `stmt_block: QCallable`

Operator `control` takes a qubit array of length one or more as `ctrl`, and applies the `stmt_block` operand if all qubits are in the `1` state

## Example

The following example shows how to use the `control` operator to implement a Multi-Control-X where a 7-qubit quantum variable serves as the control

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


@qfunc
def main(cntrl: Output[QArray[QBit]], target: Output[QBit]) -> None:
    allocate(7, cntrl)
    allocate(target)
    control(ctrl=cntrl, stmt_block=lambda: X(target))
```

```python theme={null}

qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)
```

## References

<a name="1">\[1]</a> A.

Barenco et al, Elementary gates for quantum computation,
Phys. Rev. A 52 (1995). [https://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.3457](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.3457)

<a name="2">\[2]</a> D. Maslov, Advantages of using relative-phase Toffoli gates
with an application to multiple control Toffoli optimization,
Phys. Rev. A 93 (2016). [https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.022311](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.022311)