Open Access

ARTICLE

A Technical Note for a Shor’s Algorithm by Phase Estimation

by Gérard Fleury, Philippe Lacomme^*

Université Clermont-Auvergne, Clermont-Auvergne-INP, LIMOS – UMR CNRS 6158, 1 rue de la Chébarde, 63178, Aubière Cedex, France

* Corresponding Author: Philippe Lacomme. Email:

Journal of Quantum Computing 2022, 4(2), 97-111. https://doi.org/10.32604/jqc.2022.032973

Received 03 June 2022; Accepted 23 March 2023; Issue published 16 May 2023

Abstract

The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on 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). 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 gates to efficient 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. The shor’s algorithm based on phase estimation succeeds in factoring integer numbers with more than 35 digits using circuits with about 100 qubits.

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Keywords

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