Quantum walking in curved spacetime: discrete metric
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2018-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2018-08-22-84/pdf/ |
| _version_ | 1819107134199037952 |
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| author | Pablo Arrighi Giuseppe Di Molfetta Stefano Facchini |
| author_facet | Pablo Arrighi Giuseppe Di Molfetta Stefano Facchini |
| author_sort | Pablo Arrighi |
| collection | DOAJ |
| description | A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the $(1+1)-$dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators-differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other. |
| first_indexed | 2024-12-22T02:49:12Z |
| format | Article |
| id | doaj.art-d9be55cea92648179c7332bcdb287c37 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-22T02:49:12Z |
| publishDate | 2018-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-d9be55cea92648179c7332bcdb287c372022-12-21T18:41:25ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2018-08-0128410.22331/q-2018-08-22-8410.22331/q-2018-08-22-84Quantum walking in curved spacetime: discrete metricPablo ArrighiGiuseppe Di MolfettaStefano FacchiniA discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the $(1+1)-$dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators-differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.https://quantum-journal.org/papers/q-2018-08-22-84/pdf/ |
| spellingShingle | Pablo Arrighi Giuseppe Di Molfetta Stefano Facchini Quantum walking in curved spacetime: discrete metric Quantum |
| title | Quantum walking in curved spacetime: discrete metric |
| title_full | Quantum walking in curved spacetime: discrete metric |
| title_fullStr | Quantum walking in curved spacetime: discrete metric |
| title_full_unstemmed | Quantum walking in curved spacetime: discrete metric |
| title_short | Quantum walking in curved spacetime: discrete metric |
| title_sort | quantum walking in curved spacetime discrete metric |
| url | https://quantum-journal.org/papers/q-2018-08-22-84/pdf/ |
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