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- W3097471409 abstract "We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer cite{meyer2013nonlinear}, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional grid, keeping the same computational advantage BHg{with} respect to the classical algorithms. For this purpose, we have considered the free lattice Hamiltonian, with linear dispersion relation introduced by Childs and Ge cite{Childs_2014}. The numerical simulations showed that the walker finds the marked vertex in $O(N^{1/4} log^{3/4} N) $ steps, with probability $O(1/log N)$, for an overall complexity of $O(N^{1/4}log^{7/4}N)$. We also proved that there exists an optimal choice of the walker parameters to avoid that the time measurement precision affects the complexity searching time of the algorithm." @default.
- W3097471409 created "2020-11-09" @default.
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- W3097471409 date "2020-09-16" @default.
- W3097471409 modified "2023-09-27" @default.
- W3097471409 title "Searching via nonlinear quantum walk on the 2D-grid" @default.
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