Implementing random unitaries in an imperfect photonic network

TL;DR

This paper investigates the implementation of Haar-random and Fourier unitaries in photonic networks for boson sampling, highlighting challenges with fidelity and proposing optimization methods to improve performance.

Contribution

It demonstrates the limitations of current photonic implementations and introduces numerical optimization and additional beam splitters as solutions to enhance fidelity.

Findings

Reflectivity distribution skews towards low values with more modes.

Imperfect Mach-Zehnder interferometers limit fidelity.

Optimization and extra beam splitters can improve implementation fidelity.

Abstract

We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations of boson sampling. The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. A realistic implementation using Mach-Zehnder interferometers is incapable of doing this perfectly and thus has limited fidelity. We show that numerical optimisation and adding extra beam splitters to the network can help to restore fidelity.