License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.14
URN: urn:nbn:de:0030-drops-62975
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6297/
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Fefferman, Bill ; Kobayashi, Hirotada ; Yen-Yu Lin, Cedric ; Morimae, Tomoyuki ; Nishimura, Harumichi

Space-Efficient Error Reduction for Unitary Quantum Computations

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Abstract

This paper presents a general space-efficient method for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundness s, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most 2^{-p}, the most space-efficient method known requires extra workspace of O(p*log(1/(c-s))) qubits. This space requirement is too large for scenarios like logarithmic-space quantum computations. This paper shows an errorreduction method for unitary quantum computations (i.e., computations without intermediate measurements) that requires extra workspace of just O(log(p/(c-s))) qubits. This in particular gives the first method of strong amplification for logarithmic-space unitary quantum computations with two-sided bounded error. This also leads to a number of consequences in complexity theory, such as the uselessness of quantum witnesses in bounded-error logarithmic-space unitary quantum computations, the PSPACE upper bound for QMA with exponentially-small completeness-soundness gap, and strong amplification for matchgate computations.

BibTeX - Entry

@InProceedings{fefferman_et_al:LIPIcs:2016:6297,
  author =	{Bill Fefferman and Hirotada Kobayashi and Cedric Yen-Yu Lin and Tomoyuki Morimae and Harumichi Nishimura},
  title =	{{Space-Efficient Error Reduction for Unitary Quantum Computations}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6297},
  URN =		{urn:nbn:de:0030-drops-62975},
  doi =		{10.4230/LIPIcs.ICALP.2016.14},
  annote =	{Keywords: space-bounded computation, quantum Merlin-Arthur proof systems, error reduction, quantum computing}
}

Keywords: space-bounded computation, quantum Merlin-Arthur proof systems, error reduction, quantum computing
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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