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Frontiers in Optics

Measuring the quality of boson samplers in the sparse regime

Jelmer J. Renema, Hui Wang, Jian Qin, Xiang You, Chao‐Yang Lu, Jian-Wei Pan

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We show a method for assessing the quality of photonic quantum interference (boson sampling) in the regime of fewer samples than outcomes. We present an error budget for a state of the art boson sampler.
DOI
10.1364/fio.2020.ftu6d.2

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Verification of a quantum advantage in the presence of noise is a key open problem in the study of near-term quantum devices. In this work, we show how to assess the quality of photonic interference in a linear optical quantum device (boson sampler) by using a maximum likelihood method to measure the strength at which various noise sources are present in the experiment. This allows us to use a sparse set of samples to test whether a given boson-sampling experiment meets known upper bounds on the level of noise permissible to demonstrate a quantum advantage. Furthermore, this method allows us to monitor the evolution of noise in real time, creating a valuable diagnostic tool. Finally, we observe that sources of noise in the experiment compound, meaning that the observed value of the mutual photon indistinguishability, which is the main imperfection in our study, is an effective value taking into account all sources of error in the experiment.
Analyzing the properties of complex quantum systems is crucial for further development of quantum devices, yet this task is typically challenging and demanding with respect to the required amount of measurements. Special attention to this problem appears within the context of characterizing outcomes of noisy intermediate-scale quantum devices, which produce quantum states with specific properties so that it is expected to be hard to simulate such states using classical resources. In this work, we address the problem of characterization of a boson sampling device, which uses the interference of input photons to produce samples of nontrivial probability distributions that at certain condition are hard to obtain classically. For realistic experimental conditions the problem is to probe multiphoton interference with a limited number of the measurement outcomes without collisions and repetitions. By constructing networks on the measurement outcomes, we demonstrate the possibility to discriminate between regimes of indistinguishable and distinguishable bosons by quantifying the structures of the corresponding networks. Based on this, we propose a machine-learning-based protocol to benchmark a boson sampler with unknown scattering matrix. Notably, the protocol works in the most challenging regimes of having a very limited number of bitstrings without collisions and repetitions. As we expect, our framework can be directly applied for characterizing boson sampling devices that are currently available in experiments.
Boson Sampling represents a promising witness of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called Permanent-of-Gaussians Conjecture and has been extended to some generalizations such as scattershot Boson Sampling, approximate and lossy sampling under some reasonable constraints. However, it is still unclear how demanding these bounds are for a quantum experimental sampler. Starting from a state of the art analysis and focusing on the foreseeable practical conditions needed to reach quantum supremacy, we look at different techniques and present a more general and effective solution. We apply our approach to both the experimental suggestions presented to date and we eventually find in both cases a new threshold that is less error sensitive and experimentally more feasible.
Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.