2007/06/30 by Dave Bacon, Thomas Decker · 2 citations
Computer Science · Physics and Astronomy · #Complexity and Algorithms in Graphs #Quantum Computing Algorithms and Architecture #Stochastic Gradient Optimization Techniques #quant-ph
paper · pdf · doi:10.1103/physreva.77.032335
published as Physical Review A, 77, 032335 (2008) · 8 pages. Error in main proof fixed
arxiv created 2008/01/22 · openalex publication_date 2008/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient alternative quantum algorithms for the non-Abelian hidden-subgroup problem. Previous work has identified the optimal single-copy measurement for the hidden-subgroup problem over Abelian groups as well as for the non-Abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single-copy measurement for the hidden-subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single-copy optimal measurements for the hidden-subgroup problem.