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Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation

Search by Lackadaisical Quantum Walk with Symmetry Breaking

arXiv
Authors: Jacob Rapoza, Thomas G. Wong

Year

2021

Paper ID

61931

Status

Preprint

Abstract Read

~2 min

Abstract Words

123

Citations

N/A

Abstract

The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs, including periodic lattices, strongly regular graphs, Johnson graphs, and the hypercube. In these prior works, the weights of the self-loops preserved the symmetries of the graphs. In this paper, we show that the self-loops can break all the symmetries of vertex-transitive graphs while providing the same computational speedups. Only the weight of the self-loop at the marked vertex matters, and the remaining self-loop weights can be chosen randomly, as long as they are small compared to the degree of the graph.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2021 reference point for readers tracking recent quantum research.
  • The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2108.13856 [2] arXiv https://arxiv.org/abs/2108.13856 [3] Publisher https://arxiv.org/abs/2108.13856

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