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DOI: 10.4230/LIPIcs.ICALP.2016.14
URN: urn:nbn:de:0030-drops-62975
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6297/
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 | |
| Seminar: | 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 23.08.2016 |
