> ## 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.

# Subtraction

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  Open this notebook in GitHub to run it yourself
</Card>

Subtraction (denoted as '-') is implemented by negation and addition in 2-complement representation.

$$
a - b \longleftrightarrow a + (-b) \longleftrightarrow a + \sim{b} + lsb\_value
$$

Where '\~' is bitwise not and $lsb\_value$ is the least significant bit value.

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 = 8 , 0101 + 0011 = 1000

5 - 3 = 5 + (-3) = 2, 0101 + 1101 = 0010

-5 + -3 = -8, 1011 + 1101 = 1000

## Examples

#

### Example 1: Subtraction of Two Quantum Variables

This example generates a quantum program that subtracts one quantum variables from the other, both of size 3 qubits.

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


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    b |= 5
    res |= a - b


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)

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

<Info>
  **Output:**

  ```
  [{'a': 4.0, 'b': 5.0, 'res': -1.0}: 1000]
    

  ```
</Info>

#

### Example 2: Subtraction of a Float from a Register

This example generates a quantum program which subtracts two argument.

The left\_arg is defined to be a fix point number $(11.1)_2$ (3.5).

The right\_arg is defined to be a quantum register of size of three.

```python theme={null}
@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    res |= a - 3.5


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)

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

<Info>
  **Output:**

  ```
  [{'a': 4.0, 'res': 0.5}: 1000]
    

  ```
</Info>