Efficient verification of Boson Sampling

Ulysse Chabaud1, Frédéric Grosshans1, Elham Kashefi1,2, and Damian Markham1,3

1Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
2School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB
3JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan

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Abstract

The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. Here we derive an efficient protocol for verifying with single-mode Gaussian measurements the output states of a large class of continuous-variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous-variable multimode quantum states.


Recording of conference talk at the 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021), July 5-8, 2021, University of Latvia, Riga, Latvia.

We often hear that quantum computers will offer dramatic advantages over their classical counterparts, but how can we be so sure? Well, factoring integers is hard with a classical computer, but easy with a quantum computer, so let us factor large integers and prove that quantum computers are truly powerful! There is a catch, however: quantum computers are hard to build, and we do not (yet) have quantum computers powerful enough to convincingly run a factoring algorithm on large integers.
On the other hand, we can build simpler quantum machines, such as the so-called Boson Sampling interferometers, that already challenge classical processors. Then all we need to do is to verify that these machines do what they are supposed to do…
It turns out that verifying subuniversal quantum models such as Boson Sampling is highly non-trivial, due to the nature of the computational task performed. Here we give a solution to this long-standing open problem, where verification is performed using simple Gaussian measurements available in the lab. Our results also have applications for the efficient certification of multimode continuous-variable quantum states.

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[1] Mattia Walschaers, "Non-Gaussian Quantum States and Where to Find Them", PRX Quantum 2 3, 030204 (2021).

[2] Ulysse Chabaud, Ganaël Roeland, Mattia Walschaers, Frédéric Grosshans, Valentina Parigi, Damian Markham, and Nicolas Treps, "Certification of Non-Gaussian States with Operational Measurements", PRX Quantum 2 2, 020333 (2021).

[3] Ulysse Chabaud, "Continuous Variable Quantum Advantages and Applications in Quantum Optics", arXiv:2102.05227.

[4] Ninnat Dangniam, Yun-Guang Han, and Huangjun Zhu, "Optimal verification of stabilizer states", Physical Review Research 2 4, 043323 (2020).

[5] Michał Oszmaniec, Ninnat Dangniam, Mauro E. S. Morales, and Zoltán Zimborás, "Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states", arXiv:2012.15825.

[6] Ya-Dong Wu, Ge Bai, Giulio Chiribella, and Nana Liu, "Efficient Verification of Continuous-Variable Quantum States and Devices without Assuming Identical and Independent Operations", Physical Review Letters 126 24, 240503 (2021).

[7] Ulysse Chabaud, Pierre-Emmanuel Emeriau, and Frédéric Grosshans, "Witnessing Wigner Negativity", arXiv:2102.06193.

[8] Ye-Chao Liu, Jiangwei Shang, and Xiangdong Zhang, "Efficient verification of entangled continuous-variable quantum states with local measurements", Physical Review Research 3 4, L042004 (2021).

[9] Paulina Lewandowska, Aleksandra Krawiec, Ryszard Kukulski, Łukasz Pawela, and Zbigniew Puchała, "On the optimal certification of von Neumann measurements", Scientific Reports 11, 3623 (2021).

[10] Sritam Kumar Satpathy, Vallabh Vibhu, Sudev Pradhan, Bikash K. Behera, and Prasanta K. Panigrahi, "Efficient Verification of Boson Sampling Using a Quantum Computer", arXiv:2108.03954.

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