Modulo - Classiq Docs

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The modulo operation (denoted as ’%’) returns the remainder (called “modulus”) of a division. Given two numbers

a

and

n

, the result of (

a \% n

) is the remainder of the division of a by n. The modulo operation is supported only for

n = 2^m

for an integer

m

, its result is the

m

least significant bits. For example, the binary representation of the number

53

0b110101

. The expression (

53 \% 8

) equals

0b101 = 5

, because

8 = 2^3

, which means only accounting for the

3

least significant bits of

53

Implementation in Expressions

If an expression is defined using a modulo operation, the output size is set recursively to all of its subexpressions. But if for some sub-expressions, another modulo operation is used, the sub-expression’s output_size is determined by the minimal value between the output_size of the sub-expression and the expression. See this example:

(((a + b) \% 4) + (c + d)) \% 8

. The result of expression

a + b

is saved on a two-qubit register, and the results of expressions

c + d

and

((a + b) \% 4) + (c + d)

are saved using three qubits each.

Example

This example generates a quantum program that adds two five-qubit arguments: a on qubits 0-4, and b on qubits 5-

The adder result should have been calculated on a 6-qubit register. However, the modulo operation decides that the output register of the adder only contains its two least significant qubits. Thus, the adder result is written to a two-qubit register, on qubits 10-

from classiq import *


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    allocate(5, a)
    allocate(5, b)

    a ^= 4
    b ^= 7

    res |= (a + b) % 4

qprog = synthesize(main)

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

Output:

[{'a': 4.0, 'b': 7.0, 'res': 3.0}: 1000]

Modular Exponentiation Multiplication

⌘I

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​Implementation in Expressions

​Example

Implementation in Expressions

Example