Bibliographic Details
| Title: |
Generalized quantum-classical correspondence for random walks on graphs |
| Authors: |
Frigerio, Massimo, Benedetti, Claudia, Olivares, Stefano, Paris, Matteo G. A. |
| Source: |
Phys. Rev. A 104, 030201 (2021) |
| Publication Year: |
2021 |
| Collection: |
Quantum Physics |
| Subject Terms: |
Quantum Physics |
| More Details: |
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.
Comment: 4 pages (bibliography excluded) + 3 pages of supplemental material |
| Document Type: |
Working Paper |
| DOI: |
10.1103/PhysRevA.104.L030201 |
| Access URL: |
http://arxiv.org/abs/2104.10091 |
| Accession Number: |
edsarx.2104.10091 |
| Database: |
arXiv |
