# Comparators

The following comparators are supported:

• Equal (denoted as '==')

• NotEqual (denoted as '!=')

• GreaterThan (denoted as '>')

• GreaterEqual (denoted as '>=')

• LessThan (denoted as '<')

• LessEqual (denoted as '<=')

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) = 0

(5 == 5) = 1

($$(011)_2$$ == $$(11)_2$$) = 1

(signed $$(101)_2$$ < unsigned $$(101)_2$$) = 1

## Examples

#### Example 1: Comparing Two Quantum Variables

This example generates a quantum program that performs 'equal' between two variables. The left arg is a signed variable with 5 qubits and the right arg is an unsigned varialbe with 3 qubits.

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

@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)

res |= a == b

qmod = create_model(main)

from classiq import execute, synthesize, write_qmod

write_qmod(qmod, "comparator_2vars_example")
qprog = synthesize(qmod)


#### Example 2: Comparing Integer and Quantum Variable

This example generates a quantum program that performs 'less equal' between a quantum register and an integer. The left arg is an unsigned quantum variable with 3 qubits, and the right arg is an integer equal to 2.

from classiq import (
Output,
QArray,
QBit,
QNum,
allocate,
create_model,
qfunc,
)

@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
allocate(3, a)
res |= a <= 2

qmod = create_model(main)

from classiq import execute, synthesize, write_qmod

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

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

[{'a': 4.0, 'res': 0.0}: 150,
{'a': 1.0, 'res': 1.0}: 138,
{'a': 7.0, 'res': 0.0}: 132,
{'a': 2.0, 'res': 1.0}: 126,
{'a': 6.0, 'res': 0.0}: 123,
{'a': 3.0, 'res': 0.0}: 115,
{'a': 5.0, 'res': 0.0}: 110,
{'a': 0.0, 'res': 1.0}: 106]