Search by lackadaisical quantum walk with symmetry breaking

Jacob Rapoza, Thomas G. Wong

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number062211
JournalPhysical Review A
Volume104
Issue number6
DOIs
StatePublished - Dec 2021

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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