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It has been shown classically that combining two chaotic random walks canyield an ordered(periodic) walk. Our aim in this paper is to find a quantumanalog for this rather counter-intuitive result. We study chaotic and periodicnature of cyclic quantum walks and focus on a unique situation wherein aperiodic quantum walk on a 3-cycle graph is generated via a deterministiccombination of two chaotic quantum walks on the same graph. We extend ourresults to even-numbered cyclic graphs, specifically a 4-cycle graph too. Ourresults will be relevant in quantum cryptography and quantum chaos control.

Order from chaos in quantum walks on cyclic graphs