Quantum search of spatial regions (extended abstract)

被引:97
作者
Aaronson, S [1 ]
Ambainis, A [1 ]
机构
[1] Univ Calif Berkeley, Berkeley, CA 94720 USA
来源
44TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 2003年
关键词
D O I
10.1109/SFCS.2003.1238194
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Can Grover's quantum search algorithm speed up search of a physical region-for example a 2-D grid of size rootn x rootn? The problem is that rootn time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in time O(rootn) for d greater than or equal to 3, or O(rootn log(3) n) for d = 2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include almost tight upper and lower bounds for many search tasks; a generalized algorithm that works for any graph with good expansion properties, not just hypercubes; and relationships among several notions of 'locality' for unitary matrices acting on graphs. As an application of our results, we give an O(rootn)-qubit communication protocol for the disjointness problem, which improves an upper bound of Hoyer and de Wolf and matches a lower bound of Razborov.
引用
收藏
页码:200 / 209
页数:10
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