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• W2949779675 abstract "One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden subgroup problem. As a consequence of the bounds, we show that the sample complexity for both of the decision and identification versions is $Theta(log|HH|/log p)$ for a candidate set $HH$ of hidden subgroups in the case that the candidate subgroups have the same prime order $p$, which implies that the decision version is at least as hard as the identification version in this case. In particular, it does so for the important instances such as the dihedral and the symmetric hidden subgroup problems. Moreover, the upper bound of the identification is attained by the pretty good measurement. This shows that the pretty good measurement can identify any hidden subgroup of an arbitrary group with at most $O(log|HH|)$ samples." @default.
• W2949779675 created "2019-06-27" @default.
• W2949779675 creator A5024624998 @default.
• W2949779675 creator A5069935086 @default.
• W2949779675 creator A5079746997 @default.
• W2949779675 date "2006-04-24" @default.
• W2949779675 modified "2023-09-27" @default.
• W2949779675 title "Quantum Measurements for Hidden Subgroup Problems with Optimal Sample Complexity" @default.
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• W2949779675 hasPublicationYear "2006" @default.
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