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arXiv 1102.3628quant-ph
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量子搜索问题的测试态方法

Test-State Approach to the Quantum Search Problem

Arun Sehrawat, Le Huy Nguyen, Berthold-Georg Englert

备注：
11 pages, 5 figures
发表信息：
Phys. Rev. A 83, 052311 (2011)
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摘要：

寻找“量子干草堆中的量子针”是一个比喻的问题，找出哪一个允许的一组酉映射-神谕-是由一个给定的黑盒子实现的。Grover的算法解决了这个问题，与类似的“经典大海捞针”搜索相比，速度提高了两倍。由于Grover算法的结果是概率性的-它以高概率给出正确答案，而不是确定性-答案需要验证。为此，我们引入特定的测试状态，每个oracle一个。这些测试状态也可以用来实现“量子针的经典搜索”，这是确定的-它总是在有限的步骤之后给出一个确定的答案-并且比纯经典搜索快3.41倍。由于测试状态搜索和Grover算法寻找相同的量子针，测试状态搜索的平均Oracle查询数是Grover算法的经典基准。

英文摘要：

The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this problem with quadratic speed-up as compared with the analogous search for "a classical needle in a classical haystack." Since the outcome of Grover's algorithm is probabilistic---it gives the correct answer with high probability, not with certainty---the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize "a classical search for the quantum needle" which is deterministic---it always gives a definite answer after a finite number of steps---and faster by a factor of 3.41 than the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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