The quantum query complexity of the hidden subgroup problem is polynomial

Authors:
Mark Ettinger;Peter Høyer;Emanuel Knill
Affiliations:
Los Alamos National Laboratory, Los Alamos, NM;Department of Computer Science, University of Calgary, Canada T2N 1N4;Los Alamos National Laboratory, Los Alamos, NM
Venue:
Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
Year:
2004

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Abstract

We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm. However our quantum algorithm requires exponential time, as in the classical case. Our algorithm utilizes a new technique for constructing error-free algorithms for non-decision problems on quantum computers.