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Quantum Simulation

Lackadaisical quantum walk for spatial search

arXiv

Authors: Pulak Ranjan Giri, Vladimir Korepin

Year

2018

Paper ID

23333

Status

Preprint

Abstract Read

~2 min

Abstract Words

137

Citations

N/A

Abstract

Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical quantum walk on one- and two-dimensions. It is observed that specific values of the self-loop weight at each vertex of the graph is responsible for such speedup of the algorithm. Searching for a target state on one-dimensional lattice with periodic boundary conditions is possible using lackadaisical quantum walk, which can find a target state with mathcal{O}(1) success probability after mathcal{O} left\(N right\) time steps. In two-dimensions, our numerical simulation upto M=6 suggests that lackadaisical quantum walk can search one of the M target states in mathcal{O}left\(sqrt{frac{N}{M}log frac{N}{M}}right\) time steps.

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Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1811.06169 [2] arXiv https://arxiv.org/abs/1811.06169 [3] Publisher https://arxiv.org/abs/1811.06169

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