A quantum algorithm for greatest common divisor problem

TL;DR

This paper introduces a quantum algorithm for solving the GCD problem, leveraging hidden subgroup problem techniques similar to Shor's algorithm, and provides circuit implementations and simulations.

Contribution

It presents a quantum algorithm for GCD that matches classical complexity and details explicit quantum circuits and simulations.

Findings

Quantum GCD algorithm has similar complexity to classical methods.

Explicit quantum circuits for GCD are constructed.

Simulations confirm expected quantum outcomes.

Abstract

We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This algorithm is an application of the quantum algorithms for the hidden subgroup problems, the same as Shor factoring algorithm. Explicit quantum circuits realized by quantum gates for this quantum algorithm are provided. We also give a computer simulation of this quantum algorithm and present the expected outcomes for the corresponding quantum circuit.