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 electromagnetic vector potential for a charged walker.

Generalized quantum-classical correspondence for random walks on graphs / M. Frigerio, C. Benedetti, S. Olivares, M.G.A. Paris. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 104:3(2021 Sep 16), pp. L030201.1-L030201.5. [10.1103/PhysRevA.104.L030201]

Generalized quantum-classical correspondence for random walks on graphs

M. Frigerio
Primo
;
C. Benedetti
Secondo
;
S. Olivares
Penultimo
;
M.G.A. Paris
Ultimo
2021

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 electromagnetic vector potential for a charged walker.
continuous-time quantum walks; random walks; gauge symmetries; graph theory
Settore FIS/03 - Fisica della Materia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/870123
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