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• W3037940797 abstract "First-order truncated simplex lattices have been used as interesting data structures to explore the properties of quantum search such as the effect of connectivity on search speed [D. A. Meyer and T. G. Wong, Phys. Rev. Lett. 114, 110503 (2015)]. In this paper, we further discuss quantum search algorithms for truncated simplex lattices. We first propose a multistage quantum algorithm for an $rmathrm{th}$-order truncated simplex lattice with $N$ vertices based on the numerical calculation up to the fifth-order lattice, which requires an $(r+1)$-stage search process and consumes a run time $mathrm{ensuremath{Theta}}({N}^{(2r+1)/(2r+2)})$ in general. Furthermore, with edge weights suitably adjusted (which increases the connectivity according to certain definitions), we merge the multistage search process into a single stage and achieve a fast quantum search algorithm with an optimal run time $mathrm{ensuremath{Theta}}(sqrt{N})$ for first-order truncated simplex lattices, which we conjecture is generally true for any-order lattice. Under small noise of the lattice structure, both our multistage and our single-stage search algorithms are quite robust." @default.
• W3037940797 created "2020-07-02" @default.
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• W3037940797 date "2020-06-24" @default.
• W3037940797 modified "2023-10-13" @default.
• W3037940797 title "Optimal quantum search on truncated simplex lattices" @default.
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• W3037940797 doi "https://doi.org/10.1103/physreva.101.062333" @default.
• W3037940797 hasPublicationYear "2020" @default.
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