Bitwise Xor

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The Bitwise Xor (denoted as '^') is implemented by applying this truth table between each pair of qubits (or qubit and bit) in variables 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 variable size mismatch.

For example, the positive signed number \((110)_2=6\) is expressed as \((00110)_2\) when operating with a five-qubit variable. 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

Examples

Example 1: Two Quantum Variables

This example generates a quantum program that performs bitwise 'xor' between two variables. The left arg is a signed with five qubits and the right arg is unsigned with three qubits.

from classiq import *


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    allocate_num(5, True, 0, a)
    allocate_num(3, False, 0, b)
    a ^= 4
    b ^= 5
    res |= a ^ b


qmod = create_model(main, out_file="bitwise_xor_2vars_example")

qprog = synthesize(qmod)

result = execute(qprog).result_value()
print(result.parsed_counts)
print(result.counts_of_multiple_outputs(["a", "b", "res"]))

[{'a': 4.0, 'b': 5.0, 'res': 1.0}: 1000]
{('00100', '101', '10000'): 1000}

Example 2: Integer and Quantum Variable

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

@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    res |= 3 ^ a


qmod = create_model(main, out_file="bitwise_xor_integer_example")

qprog = synthesize(qmod)

result = execute(qprog).result_value()
result.parsed_counts

[{'a': 4.0, 'res': 7.0}: 1000]