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Bitwise Xor

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

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

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 = 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] (see RegisterUserInput)
  • right_arg: Union[int, RegisterUserInput] (see RegisterUserInput)
  • output_size: Optional[PositiveInt]
  • inplace_arg: Optional[str] = None

Register names:

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

Example 1: Two Registers

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

from classiq import Model, QUInt, QSInt, synthesize
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 = Model()
model.BitwiseXor(params)
quantum_program = synthesize(model.get_model())

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

img_9.png

Example 2: Integer and Register

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

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

params = BitwiseXor(left_arg=3, right_arg=RegisterUserInput(size=3))
model = Model()
model.BitwiseXor(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.

img_10.png