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Test of Quantumness with Small-Depth Quantum Circuits

Authors Shuichi Hirahara, François Le Gall

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Author Details

Shuichi Hirahara
  • National Institute of Informatics, Tokyo, Japan
François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan

Funding

JSPS KAKENHI grants Nos. JP19H04066, JP20H05966, JP20H00579, JP20H04139, JP21H04879 and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) grants No. JPMXS0118067394 and JPMXS0120319794.

Acknowledgements

The authors are grateful to Ryo Hiromasa, Tomoyuki Morimae, Yasuhiko Takahashi and Seiichiro Tani for helpful discussions.

Cite As Get BibTex

Shuichi Hirahara and François Le Gall. Test of Quantumness with Small-Depth Quantum Circuits. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 59:1-59:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.59

Abstract

Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but cannot be solved by a classical polynomial-time computer under the LWE assumption. This test has lead to several cryptographic applications. In particular, it has been applied to producing certifiable randomness from a single untrusted quantum device, self-testing a single quantum device and device-independent quantum key distribution. 
In this paper, we show that this test of quantumness, and essentially all the above applications, can actually be implemented by a very weak class of quantum circuits: constant-depth quantum circuits combined with logarithmic-depth classical computation. This reveals novel complexity-theoretic properties of this fundamental test of quantumness and gives new concrete evidence of the superiority of small-depth quantum circuits over classical computation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum computing
  • small-depth circuits
  • quantum cryptography

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