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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.

img_9.png

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.

img_10.png