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Space-Efficient Error Reduction for Unitary Quantum Computations

Authors Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, Harumichi Nishimura

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Bill Fefferman
Hirotada Kobayashi
Cedric Yen-Yu Lin
Tomoyuki Morimae
Harumichi Nishimura

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Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, and Harumichi Nishimura. Space-Efficient Error Reduction for Unitary Quantum Computations. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ICALP.2016.14

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.
Keywords
  • space-bounded computation
  • quantum Merlin-Arthur proof systems
  • error reduction
  • quantum computing

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