2026-07-24T00:34:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14499 2024-03-06T10:54:10Z ddc:004 open_access

Test of Quantumness with Small-Depth Quantum Circuits Hirahara, Shuichi Le Gall, François Quantum computing small-depth circuits quantum cryptography 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shuichi Hirahara and François Le Gall 2021 Is Part Of LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2021.59 urn:nbn:de:0030-drops-144996 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.59 eng https://creativecommons.org/licenses/by/4.0/legalcode