[Paper Review] Efficient validation of Boson Sampling from binned photon-number distributions

Benoit Seron, Leonardo Novo+2 more|arXiv (Cornell University)|Dec 19, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper proposes a scalable, efficient validation method for boson sampling experiments based on binned photon-number distributions across output modes. By analyzing how photons distribute among grouped output modes, the method detects key imperfections—especially partial distinguishability—using polynomially scaling samples and post-processing, outperforming prior tests in sensitivity and practicality for near-term quantum devices.

ABSTRACT

In order to substantiate claims of quantum computational advantage, it is crucial to develop efficient methods for validating the experimental data. We propose a test of the correct functioning of a boson sampler with single-photon inputs that is based on how photons distribute among partitions of the output modes. Our method is versatile and encompasses previous validation tests based on bunching phenomena, marginal distributions, and even some suppression laws. We show via theoretical arguments and numerical simulations that binned-mode photon number distributions can be used in practical scenarios to efficiently distinguish ideal boson samplers from those affected by realistic imperfections, especially partial distinguishability of the photons.

Motivation & Objective

• To develop a practical and efficient validation test for boson sampling experiments that can distinguish ideal quantum devices from noisy ones.
• To address the challenge of validating near-term quantum devices where classical simulation becomes feasible under realistic noise, especially partial distinguishability of photons.
• To provide a method that is sensitive to high-order multiphoton interference, the core of boson sampling's quantum advantage.
• To ensure the validation test scales efficiently in both sample and computational resources, suitable for experimental implementation.
• To generalize and unify existing validation approaches—such as bunching, marginal distributions, and suppression laws—under a single binned distribution framework.

Proposed method

• The method uses binned output mode distributions, grouping output modes into partitions to analyze photon distribution patterns.
• It computes group-count probabilities (binned photon-number distributions) using a formalism based on permanents and Fourier-like components, avoiding phase space averages.
• The approach leverages theoretical bounds and numerical simulations to assess sensitivity to noise, particularly partial distinguishability and photon loss.
• The validation test is designed to be applicable to arbitrary linear interferometers drawn from the Haar measure, ensuring generality.
• It employs a polynomial scaling in the number of samples required to detect deviations from ideal behavior, enabling practical use with moderate data.
• The method is implemented in a user-friendly Julia package, BosonSampling.jl, supporting various noise models and experimental configurations.

Experimental results

Research questions

• RQ1 Can binned photon-number distributions be used to efficiently validate boson sampling experiments under realistic noise conditions?
• RQ2 How sensitive is the binned distribution method to partial distinguishability of input photons, a key noise source in photonic quantum devices?
• RQ3 Does the method maintain high sensitivity to high-order multiphoton interference while scaling polynomially in sample and computational cost?
• RQ4 Can the binned distribution approach unify and outperform existing validation tests such as bunching, marginal distributions, and suppression laws?
• RQ5 To what extent can binned distributions be used to probe the degree of photon indistinguishability in symmetric interferometers like the Fourier transform?

Key findings

• The binned photon-number distribution method successfully detects deviations from ideal boson sampling due to partial distinguishability with polynomially scaling sample complexity.
• Numerical simulations confirm that the method is highly sensitive to high-order multiphoton interference, which underpins the classical hardness of boson sampling.
• The approach generalizes and unifies previous validation techniques, including bunching phenomena, marginal distributions, and suppression laws, under a single framework.
• The method remains computationally efficient and scalable, making it suitable for near-term experimental validation with limited data.
• The formalism enables efficient computation of group-count probabilities without relying on phase space averages, differing from prior approaches in Gaussian boson sampling.
• The method has been integrated into the open-source BosonSampling.jl package, already used in experimental boson sampling setups.