> ## 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.

# Comparators

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

The following comparators are supported:

* Equal (denoted as '==')
* NotEqual (denoted as '!=')
* GreaterThan (denoted as '>')
* GreaterEqual (denoted as '>=')
* LessThan (denoted as '\<')
* LessEqual (denoted as '\<=')

Note that integer and fixed-point numbers are represented in a 2-complement method during function evaluation.

The binary number is extended in the case of a register size miss-match.

For example, the positive signed number $(110)_2=6$ is expressed as $(00110)_2$ when operating with a 5-qubit register.
Similarly, the negative signed number $(110)_2=-2$ is expressed as $(11110)_2$.

Examples:

(5 \<= 3) = 0

(5 == 5) = 1

($(011)_2$ == $(11)_2$) = 1

(signed $(101)_2$ \< unsigned $(101)_2$) = 1

## Examples

#

### Example 1: Comparing Two Quantum Variables

This example generates a quantum program that performs 'equal' between two variables.

The left arg is a signed variable with 5 qubits and the right arg is an unsigned varialbe with 3 qubits.

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


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    allocate(5, True, 0, a)
    allocate(3, False, 0, b)

    res |= a == b


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)
```

#

### Example 2: Comparing Integer and Quantum Variable

This example generates a quantum program that performs 'less equal' between a quantum register and an integer.

The left arg is an unsigned quantum variable with 3 qubits, and the right arg is an integer equal to

2.

```python theme={null}
@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    allocate(3, a)
    hadamard_transform(a)
    res |= a <= 2


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)

result = execute(qprog).result_value()
result.parsed_counts
```

<Info>
  **Output:**

  ```
  [{'a': 4.0, 'res': 0.0}: 150,
     {'a': 1.0, 'res': 1.0}: 138,
     {'a': 7.0, 'res': 0.0}: 132,
     {'a': 2.0, 'res': 1.0}: 126,
     {'a': 6.0, 'res': 0.0}: 123,
     {'a': 3.0, 'res': 0.0}: 115,
     {'a': 5.0, 'res': 0.0}: 110,
     {'a': 0.0, 'res': 1.0}: 106]
    

  ```
</Info>