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
Examples
Example 1: Two Quantum Variables
This example generates a quantum program that performs a bitwise 'and' between two variables, both are unsigned integer
from classiq import *
@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
prepare_int(4, a)
prepare_int(5, b)
res |= a & b
qmod = create_model(main, out_file="bitwise_and_2vars_example")
qprog = synthesize(qmod)
result = execute(qprog).result_value()
result.parsed_counts
[{'a': 4.0, 'b': 5.0, 'res': 4.0}: 1000]
Example 2: Integer and Quantum Variable
This example generates a quantum program that performs a bitwise 'and' between a quantum variable and an integer. The left arg is an integer equal to 3 and the right arg is an unsigned quantum variable with three qubits.
@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
prepare_int(5, a)
res |= 3 & a
qmod = create_model(main, out_file="bitwise_and_integer_example")
qprog = synthesize(qmod)
result = execute(qprog).result_value()
result.parsed_counts
[{'a': 5.0, 'res': 1.0}: 1000]