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- W4299303325 abstract "We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh (quant-ph/0402107) takes O(sqrt{N log N}) steps and finds a marked location with probability O(1/log N) for grid of size sqrt{N} * sqrt{N}. This probability is small, thus amplitude amplification is needed to achieve Theta(1) success probability. The amplitude amplification adds an additional O(sqrt{log N}) factor to the number of steps, making it O(sqrt{N} log N). In this paper, we show that despite a small probability to find a marked location, the probability to be within an O(sqrt{N}) neighbourhood (at an O(sqrt[4]{N}) distance) of the marked location is Theta(1). This allows to skip amplitude amplification step and leads to an O(sqrt{log N}) speed-up. We describe the results of numerical experiments supporting this idea, and we prove this fact analytically." @default.
- W4299303325 created "2022-10-02" @default.
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- W4299303325 date "2011-12-14" @default.
- W4299303325 modified "2023-09-30" @default.
- W4299303325 title "Search by quantum walks on two-dimensional grid without amplitude amplification" @default.
- W4299303325 doi "https://doi.org/10.48550/arxiv.1112.3337" @default.
- W4299303325 hasPublicationYear "2011" @default.
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