# 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:

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


### Example 1: Two Register¶

{
"constraints": {
"max_width": 13,
"max_depth": 100
},
"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¶

{
"constraints": {
"max_width": 6,
"max_depth": 100
},
"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.