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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[36] Francesco Hoch, Simone Piacentini, Taira Giordani, Zhen-Nan Tian, Mariagrazia Iuliano, Chiara Esposito, Anita Camillini, Gonzalo Carvacho, Francesco Ceccarelli, Nicolò Spagnolo, Andrea Crespi, Fabio Sciarrino, and Roberto Osellame, "Reconfigurable continuously-coupled 3D photonic circuit for Boson Sampling experiments", npj Quantum Information 8 1, 55 (2022).

[37] Gabriele Bressanini, Hyukjoon Kwon, and M. S. Kim, "Noise thresholds for classical simulability of nonlinear boson sampling", Physical Review A 106 4, 042413 (2022).

[38] Kyungjoo Noh, S. M. Girvin, and Liang Jiang, "Encoding an Oscillator into Many Oscillators", Physical Review Letters 125 8, 080503 (2020).

[39] Milica Banic, Luca Zatti, Marco Liscidini, and J. E. Sipe, "Two strategies for modeling nonlinear optics in lossy integrated photonic structures", Physical Review A 106 4, 043707 (2022).

[40] Adam Bouland, Bill Fefferman, Zeph Landau, and Yunchao Liu, 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) 1308 (2022) ISBN:978-1-6654-2055-6.

[41] Alexandra E Moylett, Raúl García-Patrón, Jelmer J Renema, and Peter S Turner, "Classically simulating near-term partially-distinguishable and lossy boson sampling", Quantum Science and Technology 5 1, 015001 (2019).

[42] Fulvio Flamini, Nicolò Spagnolo, and Fabio Sciarrino, "Photonic quantum information processing: a review", Reports on Progress in Physics 82 1, 016001 (2019).

[43] Hui Wang, Wei Li, Xiao Jiang, Y. -M. He, Y. -H. Li, X. Ding, M. -C. Chen, J. Qin, C. -Z. Peng, C. Schneider, M. Kamp, W. -J. Zhang, H. Li, L. -X. You, Z. Wang, J. P. Dowling, S. Höfling, Chao-Yang Lu, and Jian-Wei Pan, "Toward Scalable Boson Sampling with Photon Loss", Physical Review Letters 120 23, 230502 (2018).

[44] Michał Oszmaniec and Daniel J. Brod, "Classical simulation of photonic linear optics with lost particles", New Journal of Physics 20 9, 092002 (2018).

[45] 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).

[46] V. S. Shchesnovich, "Noise in boson sampling and the threshold of efficient classical simulatability", Physical Review A 100 1, 012340 (2019).

[47] Jelmer J. Renema, "Marginal probabilities in boson samplers with arbitrary input states", arXiv:2012.14917, (2020).

[48] Haoyu Qi, Lukas G. Helt, Daiqin Su, Zachary Vernon, and Kamil Brádler, "Linear multiport photonic interferometers: loss analysis of temporally-encoded architectures", arXiv:1812.07015, (2018).

[49] Leonardo Banchi, W. Steven Kolthammer, and M. S. Kim, "Multiphoton Tomography with Linear Optics and Photon Counting", Physical Review Letters 121 25, 250402 (2018).

[50] Jonathan Olson, "The role of complexity theory in quantum optics—a tutorial for BosonSampling", Journal of Optics 20 12, 123501 (2018).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-08 17:58:08) and SAO/NASA ADS (last updated successfully 2023-06-08 17:58:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

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