Open Access

ARTICLE

Foundations of Photonic Quantum Computation. Part 1. Introduction to Quantum Operators

Martin Bombardelli^1,2,3, Gérard Fleury¹, Philippe Lacomme^1,*, Bogdan Vulpescu²

1 UMR 6158 LIMOS, Université Clermont Auvergne, 1 Rue de la Chébarde, Aubière, France
2 UMR 6533 LPCA, Université Clermont Auvergne, 4 Av. Blaise Pascal, Aubière, France
3 CGI 10 Rue Eric de Cromières, Clermont-Ferrand, France

* Corresponding Author: Philippe Lacomme. Email:

Journal of Quantum Computing 2026, 8, 13-54. https://doi.org/10.32604/jqc.2026.075438

Received 31 October 2025; Accepted 23 April 2026; Issue published 26 June 2026

Abstract

This work aims to present the fundamental concepts necessary for performing computations on photonic quantum computers by detailing the gates specific to this architecture and introducing the relationships between standard Pauli gates and their counterparts in photonic systems. Physical considerations related to the optical components are addressed. Theoretical aspects concerning quantum operators are presented, and applied sections demonstrating implementations using the Perceval library developed by Quandela are given. This paper provides a comprehensive, state-of-the-art description of photonic quantum gates in a formal way. The main contribution of this paper is to allow researchers with prior knowledge of the gate model of quantum computing to have a comprehensive understanding of how some photonic quantum computers work. Three optical components are used in this document: beam splitters, phase shifters and permutation components. Most of the more common quantum gates are built from the physical description of these components and the associated physical laws. Extensive focus is placed on controlled gates, which have more complicated constructions. Two different constructions of the CNOT gate are given to show how versatile photonic quantum computers can be. The main drawback of this type of controlled gate is discussed, namely the probabilistic nature of its implementation.

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Keywords

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