TY - JOUR
T1 - Space-Efficient Error Reduction for Unitary Quantum Computations
JF - 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Y1 - 2016
A1 - Bill Fefferman
A1 - Hirotada Kobayashi
A1 - Cedric Yen-Yu Lin
A1 - Tomoyuki Morimae
A1 - Harumichi Nishimura
AB -
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.
VL - 55
U4 - 14:1--14:14
SN - 978-3-95977-013-2
UR - http://drops.dagstuhl.de/opus/volltexte/2016/6297
U5 - http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.14
ER -