TY  - EJOU
AU  - Bombardelli, Martin 
AU  - Fleury, Gérard 
AU  - Lacomme, Philippe 
AU  - Vulpescu, Bogdan 

TI  - Foundations of Photonic Quantum Computation. Part 1. Introduction to Quantum Operators
T2  - Journal of Quantum Computing

PY  - 2026
VL  - 8
IS  - 1
SN  - 2579-0145

AB  - 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.
KW  - Introduction; photonic; quantum computing; encoding; gate model; physics

DO  - 10.32604/jqc.2026.075438