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arXiv · 2301.07251

No Infinite Tail Beats Optimal Spatial Search

Weichen Xie·Christino Tamon
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Abstract

Farhi and Gutmann (Physical Review A, 57(4):2403, 1998) proved that a continuous-time analogue of Grover search (also called spatial search) is optimal on the complete graphs. We extend this result by showing that spatial search remains optimal in a complete graph even in the presence of an infinitely long path (or tail). If we view the latter as an external quantum system that has a limited but nontrivial interaction with our finite quantum system, this suggests that spatial search is robust against a coherent infinite one-dimensional probe. Moreover, we show that the search algorithm is oblivious in that it does not need to know whether the tail is present or not, and if so, where it is attached to.

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Weichen Xie, Christino Tamon. 2023-01-18. No Infinite Tail Beats Optimal Spatial Search. https://doi.org/10.1103/physreva.107.032416

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