Experimental validation of boson sampling using detector binning

TL;DR

This paper presents an experimentally validated, scalable method for validating boson sampling experiments by analyzing binned photon distributions, effectively diagnosing imperfections and understanding the impact of photon distinguishability.

Contribution

It introduces a practical validation strategy based on binned distributions, demonstrated on a three-photon photonic chip with analysis of distinguishability effects.

Findings

High indistinguishability yields accurate binned distributions

Method effectively diagnoses partial distinguishability and chip imperfections

Variance of binned distributions relates to photon indistinguishability

Abstract

We experimentally demonstrate a testing strategy for boson samplers that is based on efficiently computable expressions for the output photon counting distributions binned over multiple optical modes. We apply this method to validate boson sampling experiments with three photons on a reconfigurable photonic chip, which implements a four-mode interferometer, analyzing 50 Haar-random unitary transformations while tuning photon distinguishability via controlled delays. We show that for high values of indistinguishability, the experiment accurately reproduces the ideal boson sampling binned-mode distributions, which exhibit variations that depend both on the specific interferometer implemented as well as the choice of bin, confirming the usefulness of the method to diagnose imperfections such as partial distinguishability or imperfect chip control. Finally, we analyze the behavior of Haar-averaged binned-mode distributions with partial distinguishability and demonstrate analytically that its variance is proportional to the average of the square of the photons' indistinguishability parameter. These findings highlight the central role of binning in boson sampling validation, offering a scalable and efficient framework for assessing multiphoton interference and experimental performance.