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- W2906945468 abstract "We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search algorithm with multiple target states, and determine the oracle complexity as a function of the spectral gap and the number of target states. The oracle complexity is optimal as a function of the graph size and the number of target states, when the spectral gap of the adjacency matrix is $Theta(1)$. It is also optimal for spatial search on D>4 dimensional hypercubic lattices. Otherwise it matches the best result available in the literature, with a much simpler algorithm. Our results also yield bounds on the classical hitting time of random walks on regular graphs, which may be of independent interest." @default.
- W2906945468 created "2019-01-11" @default.
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- W2906945468 date "2018-12-01" @default.
- W2906945468 modified "2023-10-16" @default.
- W2906945468 title "Spatial search using flip-flop quantum walk" @default.
- W2906945468 doi "https://doi.org/10.26421/qic18.15-16-3" @default.
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