Generalized quantum-classical correspondence for random walks on graphs

Abstract

We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We found that these conditions are satisfied by infinitely many quantum Hamiltonians, which provide novel degrees of freedom for quantum enhanced protocols, In particular, the on-site energies, i.e. the diagonal elements of H, and the phases of the off-diagonal elements are unconstrained on the quantum side. The diagonal elements represent a potential energy landscape for the quantum walk, and may be controlled by the interaction with a classical scalar field, whereas, for regular lattices in generic dimension, the off-diagonal phases of H may be tuned by the interaction with a classical gauge field residing on the edges, e.g., the electro-magnetic vector potential for a charged walker.

arXiv comment4 pages (bibliography excluded) + 3 pages of supplemental material

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Cited by in corpus (9)

• Complex networks with complex weights
• Quantum-classical distance as a tool to design optimal chiral quantum walk
• Swift chiral quantum walks
• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning
• The extended star graph as a light-harvesting-complex prototype: excitonic absorption speedup by peripheral energy defect tuning
• Decoherence and classicalization of continuous-time quantum walks on graphs
• Implementation of Continuous-Time Quantum Walks on Quantum Computers
• Perturbed graphs achieve unit transport efficiency without environmental noise
• Universality of the fully connected vertex in Laplacian continuous-time quantum walk problems