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arXiv:2008.09077 · Physical Review A

Sample-efficient benchmarking of multiphoton interference on a boson sampler in the sparse regime

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

Published Feb 26, 2021• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.103.023722

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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.
Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For such a demonstration to be meaningful, experimental noise must not affect the computational power of the device; this occurs when a classical algorithm can use the noise to simulate the quantum system. In this work, we demonstrate an algorithm which simulates boson sampling, a quantum advantage demonstration based on many-body quantum interference of indistinguishable bosons, in the presence of optical loss. Finding the level of noise where this approximation becomes efficient lets us map out the maximum level of imperfections at which it is still possible to demonstrate a quantum advantage. We show that current photonic technology falls short of this benchmark. These results call into question the suitability of boson sampling as a quantum advantage demonstration.
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single- and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.
For near-term quantum devices, an important challenge is to develop efficient methods to certify that noise levels are low enough to allow potentially useful applications to be carried out. We present such a method tailored to photonic quantum devices consisting of single photon sources coupled to linear optical circuits coupled to photon detectors. It uses the output statistics of BosonSampling experiments with input size nnn (nnn input photons in the ideal case). We propose a series of benchmark tests targetting two main sources of noise, namely photon loss and distinguishability. Our method results in a single-number metric, the Photonic Quality Factor, defined as the largest number of input photons for which the output statistics pass all tests. We provide strong evidence that passing all tests implies that our experiments are not efficiently classically simulable, by showing how several existing classical algorithms for efficiently simulating noisy BosonSampling fail the tests. Finally we show that BosonSampling experiments with average photon loss rate per mode scaling as o(1)o(1)o(1) and average fidelity of $ (1-o(\frac{1}{n^6}))^2$ between any two single photon states is sufficient to keep passing our tests. Unsurprisingly, our results highlight that scaling in a manner that avoids efficient classical simulability will at some point necessarily require error correction and mitigation.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.