21161nas a2200205 45000080041000000200022000410220014000632450069000772100068001462600015002143000016002294900007002455202053400252100002020786700002420806700002420830700002220854700002520876856005420901 2016 eng d a978-3-95977-013-2 a1868-896900aSpace-Efficient Error Reduction for Unitary Quantum Computations0 aSpaceEfficient Error Reduction for Unitary Quantum Computations c2016/04/27 a14:1--14:140 v553 aThis 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.

1 aFefferman, Bill1 aKobayashi, Hirotada1 aLin, Cedric, Yen-Yu1 aMorimae, Tomoyuki1 aNishimura, Harumichi uhttp://drops.dagstuhl.de/opus/volltexte/2016/6297