منابع مشابه
Optimal measurements for the dihedral hidden subgroup problem
We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success probability of this measurement exhibits a sharp threshold as a function of the density ν = k/ log2N , where k is the number of copies of the hidden subgrou...
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In Quantum Computation and Lattice Problems [11] Oded Regev presented the first known connection between lattices and quantum computation, in the form of a quantum reduction from the poly(n)-unique shortest vector problem to the dihedral hidden subgroup problem by sampling cosets. This article contains a summary of Regev’s result.
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In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is superpolynomial. We describe a modified algorithm whose running time is still subexponential and whose space requirement is only polynomial.
متن کاملA Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity 2O( √ log N). In this problem an oracle computes a function f on the dihedral group DN which is invariant under a hidden reflection in DN . By contrast the classical query complexity of DHSP is O( √ N). The algorithm also applies to the hidden shift problem for an arbitrary finitely generated ...
متن کاملAnother Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
We give an algorithm for the hidden subgroup problem for the dihedral group DN , or equivalently the cyclic hidden shift problem, that supersedes our first algorithm and is suggested by Regev’s algorithm. It runs in exp(O( √ logN)) quantum time and uses exp(O( √ logN)) classical space, but only O(logN) quantum space. The algorithm also runs faster with quantumly addressable classical space than...
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ژورنال
عنوان ژورنال: IPSJ Digital Courier
سال: 2005
ISSN: 1349-7456
DOI: 10.2197/ipsjdc.1.470