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Author |
Hinarejos, M.; Perez, A.; Roldan, E.; Romanelli, A.; de Valcarcel, G.J. |
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Title |
Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more |
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Journal Article |
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Year |
2013 |
Publication |
New Journal of Physics |
Abbreviated Journal |
New J. Phys. |
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Volume |
15 |
Issue |
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Pages  |
073041 - 31pp |
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Abstract |
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented. |
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Address |
[Hinarejos, Margarida; Perez, Armando] Univ Valencia, CSIC, Dept Fis Teor, E-46100 Burjassot, Spain, Email: Armando.Perez@uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1367-2630 |
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Notes |
WOS:000322110600003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1504 |
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Author |
Bru, L.A.; de Valcarcel, G.J.; Di Molfetta, G.; Perez, A.; Roldan, E.; Silva, F. |
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Title |
Quantum walk on a cylinder |
Type |
Journal Article |
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Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
94 |
Issue |
3 |
Pages |
032328 - 7pp |
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Keywords |
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Abstract |
We consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or “hidden” extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension. |
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Address |
[Bru, Luis A.] Univ Politecn Valencia, ITEAM Res Inst, Opt & Quantum Commun Grp, Camino Vera S-N, E-46022 Valencia, Spain |
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Publisher |
Amer Physical Soc |
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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2469-9926 |
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Notes |
WOS:000384060700005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2823 |
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