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Paper detail

An Improved Query for the Hidden Subgroup Problem

An equal superposition query with |0> in the response register is used in the "standard method" of single-query algorithms for the hidden subgroup problem (HSP). Here we introduce a different query, the character query, generalizing the well-known phase kickback trick. This query maximizes the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We then apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.

preprint2012arXivOpen access
Asif Shakeel
math.RTmath-phmath.MPquant-ph
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Asif Shakeel

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