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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:

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.

img_5.png

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.

img_6.png