# Bitwise Xor¶

The Bitwise Xor (denoted as '^') is implemented by applying the following truth table

a b a ^ b
0 0 0
0 1 1
1 0 1
1 1 0

between each pair of qubits (or qubit and bit) in registers A and B .

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 = 6 since 101 ^ 011 = 110

5 ^ -3 = -8 since 0101 ^ 1101 = 1000

-5 ^ -3 = 6 since 1011 ^ 1101 = 0110

## Syntax¶

Function: BitwiseXor

Parameters:

• left_arg: Union[int, RegisterUserInput]
• right_arg: Union[int, RegisterUserInput]
• output_size: Optional[PositiveInt]
• output_name: Optional[str]
• inplace_arg: Optional[str] = None
{
"function": "BitwiseXor",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}


### Register Names¶

By default, the input registers are called left_arg and right_arg. If the name field of a RegisterUserInput object is specified, then the name of the register is determined accordingly. If one of the arguments is a constant then it is not available as an input register.

The output registers include the result register. By default, it is called bitwise_xor, but its name may be overridden by the output_name argument. The inplace_arg argument sets the argument to override. If it is set to None, the input registers are also available as output registers, with the same names. If it is set to left or right, only the right or left argument will be available, respectively. The qubits of the overriden argument will be used for the result.

### Example 1: Two Register¶

{
"logic_flow": [
{
"function": "BitwiseXor",
"function_params": {
"left_arg": {
"size": 5,
"is_signed": true
},
"right_arg": {
"size": 3
}
}
}
]
}

from classiq import ModelDesigner, QUInt, QSInt
from classiq.builtin_functions import BitwiseXor

params = BitwiseXor(
left_arg=QSInt(size=5).to_register_user_input(),
right_arg=QUInt(size=3).to_register_user_input(),
)

model_designer = ModelDesigner()
model_designer.BitwiseXor(params)
circuit = model_designer.synthesize()


This example generates a circuit that performs bitwise 'xor' between two registers. The left arg is a signed register with 5 qubits and the right arg is an unsigned register with 3 qubits.

### Example 2: Integer and Register¶

{
"logic_flow": [
{
"function": "BitwiseXor",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}
]
}

from classiq import ModelDesigner
from classiq.builtin_functions import BitwiseXor
from classiq.interface.generator.arith.arithmetic import RegisterUserInput

params = BitwiseXor(left_arg=3, right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.BitwiseXor(params)
circuit = model_designer.synthesize()


This example generates a circuit that performs bitwise 'and' between a quantum register and an integer. The left arg is an integer equal to three and the right arg is unsigned quantum register with 3 qubits.