Commentary on the decomposition of universal multiport interferometers: how it works in practice

TL;DR

This paper provides a practical, mathematically detailed guide for decomposing multiport interferometers, crucial in quantum optics, with examples and phase correction techniques to facilitate implementation.

Contribution

It offers a comprehensive, self-contained reference for the decomposition process, including mathematical methods and practical examples, enhancing understanding and application.

Findings

Clear mathematical framework for decomposition

Practical examples demonstrating the process

Guidance on phase correction techniques

Abstract

The decomposition of multiport interferometers is a fundamental tool in quantum optics and computing. This note aims to serve as a concise reference for performing the decomposition according to the most common design approaches, offering a self-contained treatment with essential mathematical details and practical working examples. Specifically, we provide a clear, self-consistent presentation of all the mathematics required to determine the gate parameters and apply the necessary phase corrections to achieve the desired structure.