eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-16
21:1
21:20
10.4230/LIPIcs.CCC.2019.21
article
Average-Case Quantum Advantage with Shallow Circuits
Le Gall, François
1
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Recently Bravyi, Gosset and König (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the average-case setting that gives stronger evidence of the superiority of small-depth quantum computation: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth. Our results are obtained by introducing a technique to create quantum states exhibiting global quantum correlations from any graph, via a construction that we call the extended graph.
Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233}), and Bene Watts, Kothari, Schaeffer and Tal (STOC 2019).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol137-ccc2019/LIPIcs.CCC.2019.21/LIPIcs.CCC.2019.21.pdf
Quantum computing
circuit complexity
constant-depth circuits