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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,
    hadamard_transform,
    qfunc,
)


@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    allocate(3, a)
    hadamard_transform(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]