The quantum query complexity of the hidden subgroup problem is polynomial

Details The quantum query complexity of the hidden subgroup problem is polynomial The quantum query complexity of the hidden subgroup problem is polynomial

2004-01-14

arxiv.org/abs/quant-ph/0401083v1

Physics

Quantum Physics

To appear in Information Processing Letters (IPL)

Scientific paper

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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