A technical note for a Shor's algorithm by phase estimation

TL;DR

This paper explores the implementation of Shor's algorithm using phase estimation, focusing on modular exponentiation and introducing a linear depth unit, with numerical validation on IBM's quantum simulators.

Contribution

It presents a novel modular multiplier based on phase estimation and a linear depth circuit design for modular exponentiation in Shor's algorithm.

Findings

Successful numerical experiments on IBM's simulator

Efficient modular multiplier design based on phase estimation

Feasibility of implementing Shor's algorithm with reduced circuit depth

Abstract

The objective of this paper concerns at first the motivation and the method of Shor's algorithm including an excursion into quantum mechanics and quantum computing introducing an algorithmic description of the method. The corner stone of the Shor's algorithm is the modular exponentiation that is the most computational component (in time and space). Second, a linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a modular exponentiation circuit. Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM.