# Bitwise And¶

The Bitwise And (denoted as '&') is implemented by applying this truth table between each pair of qubits in register A and B (or qubit and bit).

a b a & b
0 0 0
0 1 0
1 0 0
1 1 1

Note that integer and fixed-point numbers are represented in a two-complement method during function evaluation. The binary number is extended in the case of a register size mismatch.

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

Examples:

5 & 3 = 1 since 101 & 011 = 001

5 & -3 = 5 since 0101 & 1101 = 0101

-5 & -3 = -7 since 1011 & 1101 = 1001

## Syntax¶

Function: BitwiseAnd

Parameters:

• left_arg: Union[int, RegisterUserInput] (see RegisterUserInput)
• right_arg: Union[int, RegisterUserInput] (see RegisterUserInput)
• output_size: Optional[PositiveInt]

Register names:

• left_arg: left_arg
• right_arg: right_arg
• result: bitwise_and
{
"function": "BitwiseAnd",
"function_params": {
"left_arg": 3,
"right_arg": { "size": 3 }
}
}


## Example 1: Two Register¶

    {
"functions": [
{
"name": "main",
"body": [
{
"function": "BitwiseAnd",
"function_params": {
"left_arg": {"size": 5, "is_signed":true},
"right_arg": {"size": 3}
}
}
]
}
]
}

from classiq import Model, RegisterUserInput, synthesize
from classiq.builtin_functions import BitwiseAnd

params = BitwiseAnd(
left_arg=RegisterUserInput(size=5, is_signed=True),
right_arg=RegisterUserInput(size=3),
)
model = Model()
model.BitwiseAnd(params)
quantum_program = synthesize(model.get_model())


This example generates a circuit that performs a bitwise 'and' between two registers. The left arg is signed with five qubits and the right arg is unsigned with three qubits. ## Example 2: Integer and Register¶

    {
"functions": [
{
"name": "main",
"body": [
{
"function": "BitwiseAnd",
"function_params": {
"left_arg": 3,
"right_arg": {"size": 3}
}
}
]
}
]
}

from classiq import Model, RegisterUserInput, synthesize
from classiq.builtin_functions import BitwiseAnd

params = BitwiseAnd(left_arg=3, right_arg=RegisterUserInput(size=3))
model = Model()
model.BitwiseAnd(params)
quantum_program = synthesize(model.get_model())


This example generates a circuit that performs a bitwise 'and' between a quantum register and an integer. The left arg is an integer equal to three and the right arg is an unsigned quantum register with three qubits. 