2019
DOI: 10.1103/physreva.100.012105
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Chirality from quantum walks without a quantum coin

Abstract: Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom-called the coin and represented by a finite-dimensional Hilbert space-is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nod… Show more

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Cited by 7 publications
(1 citation statement)
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“…[19][20][21][22][23][24][25] and the recent reviews [26,27]) which consist of a translational invariant network of local quantum gates implementing the discrete-time evolution of a discrete set of quantum systems, each one interacting only with a finite number of neighbours. QCAs and in particular Quantum Walks (QWs) [28], which can be thought of as the one particle sectors of QCAs, have been considered as a simulation tool for relativistic quantum fields [29][30][31][32][33][34] and as discrete approaches for studying the foundations of Quantum Field Theory [34][35][36][37][38].…”
mentioning
confidence: 99%
“…[19][20][21][22][23][24][25] and the recent reviews [26,27]) which consist of a translational invariant network of local quantum gates implementing the discrete-time evolution of a discrete set of quantum systems, each one interacting only with a finite number of neighbours. QCAs and in particular Quantum Walks (QWs) [28], which can be thought of as the one particle sectors of QCAs, have been considered as a simulation tool for relativistic quantum fields [29][30][31][32][33][34] and as discrete approaches for studying the foundations of Quantum Field Theory [34][35][36][37][38].…”
mentioning
confidence: 99%