Foundations of photonic quantum computation

This work aims to introduce the fundamental concepts required to perform computations on photonic quantum computers by presenting the gates specific to this architecture and highlighting the connections between standard Pauli gates and those available in photonic systems. The introduction navigates between physical considerations related to the optical components used, theoretical aspects concerning quantum operators, and a more applied section introducing implementations using the Perceval library developed by Quandela. This paper is intended for engineers and researchers familiar with Pauli gates and standard quantum concepts, looking at a clear and compact introduction to photonic components. A second part aims to introduce the concept of polarization, not from a theoretical perspective, but through its practical applications. To do so, we compare the similarities and differences between the original Grover's algorithm formulation and a version that leverages polarization. Gates specific to polarization are introduced and described in the context of the computations involved in Grover's algorithm. The description provided is as mathematical as possible and deliberately avoids physical considerations, in order to allow researchers familiar with "conventional" quantum circuits to more easily grasp the concepts.