Operating with Quantum Integers: an Efficient 'Multiples of' Oracle

TL;DR

This paper introduces an efficient quantum 'multiples of' oracle that simplifies integer operations in quantum algorithms, with linear complexity and depth, validated through theoretical analysis and empirical circuit simulations.

Contribution

It presents a novel, efficient 'multiples of' quantum oracle that enhances abstraction and reusability for quantum software development.

Findings

Circuit depth scales linearly with qubits

Classical calculation complexity is linear

Empirical circuit analysis supports theoretical results

Abstract

Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part of a broader research focused on providing operations of a higher abstraction level to manipulate integers codified as a superposition. These operations are designed to be composable and efficient, so quantum software developers can reuse them to create more complex solutions. Specifically, in this paper we present a 'multiples of' operation. To validate this operation we show several examples of quantum circuits and their simulations, including its composition possibilities. A theoretical analysis proves that both the complexity of the required classical calculations and the depth of the circuit scale linearly with the number of qubits. Hence, the 'multiples of' oracle is efficient in terms of complexity and depth. Finally, an empirical study of the circuit depth is conducted to further reinforce the theoretical analysis.