%0 Journal Article
%J 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
%D 2016
%T Space-Efficient Error Reduction for Unitary Quantum Computations
%A Bill Fefferman
%A Hirotada Kobayashi
%A Cedric Yen-Yu Lin
%A Tomoyuki Morimae
%A Harumichi Nishimura
%X
This paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundnesss, 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(plog1c−s) qubits. This space requirement is too large for scenarios like logarithmic-space quantum computations. This paper presents error-reduction methods for unitary quantum computations (i.e., computations without intermediate measurements) that require extra workspace of just O(logpc−s) qubits. This in particular gives the first methods 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.
%B 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
%V 55
%P 14:1--14:14
%8 2016/04/27
%@ 978-3-95977-013-2
%G eng
%U http://drops.dagstuhl.de/opus/volltexte/2016/6297
%R http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.14