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arXiv:2202.04735

Assessing the quality of near-term photonic quantum devices

Rawad Mezher, Shane Mansfield

Published Feb 9, 2022• 3 citations
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Abstract

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 $n$ ($n$ 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 $o(1)$ 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.

DOI
10.48550/arxiv.2202.04735

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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(1n6))2 (1-o(\frac{1}{n^6}))^2(1−o(n61​))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.
Photon loss rates set an effective upper limit on the size of computations that can be run on current linear optical quantum devices. We present a family of techniques designed to mitigate the effects of photon loss on both output probabilities and expectation values derived from noisy linear optical circuits composed of an input of n photons, an m --mode interferometer, and m single photon detectors. Central to these techniques is the construction recycled probabilities . Recycled probabilities are constructed from output statistics affected by loss, and are designed to amplify the signal of the ideal (lossless) probabilities. Classical postprocessing techniques then take recycled probabilities as input and output a set of loss-mitigated probabilities, or expectation values. Our postprocessing methods result in biased estimators of the lossless probabilities. Nevertheless, we provide both analytical and numerical evidence that these methods can be applied, up to large sample sizes, to produce output probabilities with lower combined bias and statistical errors than the statistical errors of the output probabilities obtained from postselection. Therefore, these methods can outperform postselection - currently the standard method of coping with photon loss when sampling from discrete variable linear optical quantum circuits. In contrast, we provide evidence that the popular zero-noise extrapolation technique cannot improve on the performance of postselection for any photon loss rate.
Quantum computers are inherently affected by noise. While in the long term, error correction codes will account for noise at the cost of increasing physical qubits, in the near term, the performance of any quantum algorithm should be tested and simulated in the presence of noise. As noise acts on the hardware, the classical simulation of a quantum algorithm should not be agnostic on the platform used for the computation. In this paper, we apply the recently proposed noisy gates approach to efficiently simulate noisy optical circuits described in the dual rail framework. The evolution of the state vector is simulated directly, without requiring the mapping to the density matrix framework. Notably, we test the method on both the gate-based and measurement-based quantum computing models, showing that the approach is very versatile. We also evaluate the performance of a photonic variational quantum algorithm to solve the MAX-2-CUT problem. In particular we design and simulate an ansatz, which is resilient to photon losses up to p ∼ 10 − 3 making it relevant for near-term applications. Published by the American Physical Society 2024
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.
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.
As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.
BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal for quantum computation, it remains an open question of whether any error-correction techniques can be applied to them, and thus it is important to investigate how robust the model is under natural experimental imperfections, such as losses and imperfect control of parameters. Here, we investigate the complexity of BosonSampling under photon losses, more specifically, the case where an unknown subset of the photons is randomly lost at the sources. We show that if kkk out of nnn photons are lost, then we cannot sample classically from a distribution that is $1/{n}^{\mathrm{\ensuremath{\Theta}}(k)}$ close (in total variation distance) to the ideal distribution, unless a BPPNP{\text{BPP}}^{\text{NP}}BPPNP machine can estimate the permanents of Gaussian matrices in nO(k){n}^{O(k)}nO(k) time. In particular, if kkk is constant, this implies that simulating lossy BosonSampling is hard for a classical computer, under exactly the same complexity assumption used for the original lossless case.