Order from chaos in quantum walks on cyclic graphs
This work addresses a foundational problem in quantum computing, with potential applications in quantum cryptography and chaos control, but it appears incremental as it extends a known classical result to a quantum analog.
The paper tackled the problem of generating periodic quantum walks from chaotic ones on cyclic graphs, achieving a deterministic combination of two chaotic quantum walks to produce a periodic walk on a 3-cycle graph and extending this to a 4-cycle graph.
It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.