The authors introduce a blocked loop Hafnian and finite-difference sieve that compute coarse-grained photon-number distributions of Gaussian states in exponential, not combinatorial, time.
Efficient validation of Boson Sampling from binned photon-number distributions
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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.
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Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation
The authors introduce a blocked loop Hafnian and finite-difference sieve that compute coarse-grained photon-number distributions of Gaussian states in exponential, not combinatorial, time.