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Modulo

The modulo operation (denoted as ’%’) returns the remainder (called “modulus”) of a division. Given two numbers aa and nn, the result of (a%na \% n) is the remainder of the division of a by n. The modulo operation is supported only for n=2mn = 2^m for an integer mm, its result is the mm least significant bits. For example, the binary representation of the number 5353 is 0b1101010b110101. The expression (53%853 \% 8) equals 0b101=50b101 = 5, because 8=238 = 2^3, which means only accounting for the 33 least significant bits of 5353.

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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(((a + b) \% 4) + (c + d)) \% 8. The result of expression a+ba + b is saved on a two-qubit register, and the results of expressions c+dc + d and ((a+b)%4)+(c+d)((a + b) \% 4) + (c + d) are saved using three qubits each.

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Example

This example generates a quantum program that adds two five-qubit arguments: a on qubits 0-4, and b on qubits 5-
  1. 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


qmod = create_model(main)


qprog = synthesize(qmod)

result = execute(qprog).result_value()
print(result.parsed_counts)
Output:
[{'a': 4.0, 'b': 7.0, 'res': 3.0}: 1000]