# 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 Output, QArray, QBit, QNum, create_model, prepare_int, qfunc

@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)

from classiq import execute, synthesize, write_qmod

write_qmod(qmod, "bitwise_and_2vars_example")
qprog = synthesize(qmod)

result = execute(qprog).result()[0].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.

from classiq import Output, QArray, QBit, QNum, create_model, prepare_int, qfunc

@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
prepare_int(5, a)
res |= 3 & a

qmod = create_model(main)

from classiq import execute, synthesize, write_qmod

write_qmod(qmod, "bitwise_and_integer_example")
qprog = synthesize(qmod)

result = execute(qprog).result()[0].value
result.parsed_counts

[{'a': 5.0, 'res': 1.0}: 1000]