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arXiv · 2105.05500

Test of Quantumness with Small-Depth Quantum Circuits

Shuichi Hirahara·François Le Gall
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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.

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BibTeXRIS

Shuichi Hirahara, François Le Gall. 2021-08-10. Test of Quantumness with Small-Depth Quantum Circuits. https://doi.org/10.4230/lipics.mfcs.2021.59

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