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The quantum query complexity of the hidden subgroup problem is polynomial

Mark Ettinger·Peter Hoyer·Emanuel Knill
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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.

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Mark Ettinger, Peter Hoyer, Emanuel Knill. 2004-01-14. The quantum query complexity of the hidden subgroup problem is polynomial. https://doi.org/10.1016/j.ipl.2004.01.024

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