Order from chaos in quantum walks on cyclic graphs

Abstract

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.

8 pages, 11 figures, revised with a new section on secure encryption-decryption mechanism via combining chaotic quantum walks to yield an ordered quantum walk. Accepted for publication in Physical Review A

References in corpus (3)

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Cited by in corpus (8)

• Efficient implementation of discrete-time quantum walks on quantum computers
• Parrondo's effect in continuous-time quantum walks
• Recurrent generation of maximally entangled single particle states via quantum walks on cyclic graphs
• Quantum cryptographic protocols with dual messaging system via 2D alternate quantum walk of a genuine single-photon entangled state
• Chaos and Parrondo's paradox: An overview
• Combinatorial necessary conditions for regular graphs to induce periodic quantum walks
• The simplest 2D quantum walk detects chaoticity
• Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware