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arXiv · 2108.13856

Search by Lackadaisical Quantum Walk with Symmetry Breaking

Jacob Rapoza·Thomas G. Wong
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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.

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Jacob Rapoza, Thomas G. Wong. 2021-08-31. Search by Lackadaisical Quantum Walk with Symmetry Breaking. https://doi.org/10.1103/physreva.104.062211

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