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URN: urn:nbn:de:0030-drops-108432
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Average-Case Quantum Advantage with Shallow Circuits

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Abstract

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).

BibTeX - Entry

@InProceedings{legall:LIPIcs:2019:10843,
  author =	{Fran{\c{c}}ois Le Gall},
  title =	{{Average-Case Quantum Advantage with Shallow Circuits}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Amir Shpilka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10843},
  URN =		{urn:nbn:de:0030-drops-108432},
  doi =		{10.4230/LIPIcs.CCC.2019.21},
  annote =	{Keywords: Quantum computing, circuit complexity, constant-depth circuits}
}

Keywords: Quantum computing, circuit complexity, constant-depth circuits
Seminar: 34th Computational Complexity Conference (CCC 2019)
Issue date: 2019
Date of publication: 2019


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