Simulating boson sampling in lossy architectures

Raúl García-Patrón1, Jelmer J. Renema2,3, and Valery Shchesnovich4

1Centre for Quantum Information and Communication, Ecole Polytechnique de Bruxelles, CP 165, Université Libre de Bruxelles, 1050 Brussels, Belgium
2Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
3University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
4Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, SP, 09210-170 Brazil.

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Abstract

Photon losses are among the strongest imperfections affecting multi-photon interference. Despite their importance, little is known about their effect on boson sampling experiments. In this work we show that using classical computers, one can efficiently simulate multi-photon interference in all architectures that suffer from an exponential decay of the transmission with the depth of the circuit, such as integrated photonic circuits or optical fibers. We prove that either the depth of the circuit is large enough that it can be simulated by thermal noise with an algorithm running in polynomial time, or it is shallow enough that a tensor network simulation runs in quasi-polynomial time. This result suggests that in order to implement a quantum advantage experiment with single-photons and linear optics new experimental platforms may be needed.

Demonstrating the computational advantage of a quantum over a digital computation is considered the next and most important milestone in the field of quantum computation. Such a demonstration would take the form of a competition, where the quantum and classical computers race to solve a specific computational problem. In the recent years few proposals have emerged as candidates to demonstrate the power of quantum computing. One of this problems is $\textit{boson sampling}$, which is a quantum device using the interference of particles of light (photons) to encode a computation that is believed to be difficult to carry out classically. During the operation of a realistic boson sampler, some photons can be lost to the computation – scattered out of the machine or absorbed in it. An important open question was whether this imperfect quantum computation was still hard for the classical computer to emulate. This question is answered in this work for most known architectures, which suffer from an exponential decay of the transmission with the depth of the circuit, such as integrated photonic circuits or optical fibres. This result suggests that in order to implement a quantum advantage experiment with single-photons and linear optics new experimental platforms may be needed.

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[6] William R. Clements, Jelmer J. Renema, Andreas Eckstein, Antonio A. Valido, Adriana Lita, Thomas Gerrits, Sae Woo Nam, W. Steven Kolthammer, Joonsuk Huh, and Ian A. Walmsley, "Approximating vibronic spectroscopy with imperfect quantum optics", Journal of Physics B Atomic Molecular Physics 51 24, 245503 (2018).

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