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Quantum Machine Learning Quantum State Preparation Representation

Lackadaisical quantum walks on triangular and honeycomb 2D grids

arXiv

Authors: Nikolajs Nahimovs

Year

2020

Paper ID

21987

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

Abstract

In the typical model, a discrete-time coined quantum walk search has the same running time of O\(sqrt{N} log{N}\) for 2D rectangular, triangular and honeycomb grids. It is known that for 2D rectangular grid the running time can be improved to O\(sqrt{N log{N}}\) using several different techniques. One of such techniques is adding a self-loop of weight 4/N to each vertex (i.e. making the walk lackadaisical). In this paper we apply lackadaisical approach to quantum walk search on triangular and honeycomb 2D grids. We show that for both types of grids adding a self-loop of weight 6/N and 3/N for triangular and honeycomb grids, respectively, results in O\(sqrt{N log{N}}\) running time.

Why This Paper Matters

This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
It adds a 2020 reference point for readers tracking recent quantum research.
In the typical model, a discrete-time coined quantum walk search has the same running time of O(sqrtN logN) for 2D rectangular, triangular and honeycomb grids.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2007.13564 [2] arXiv https://arxiv.org/abs/2007.13564 [3] Publisher https://arxiv.org/abs/2007.13564

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