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Author  |
Arnault, P.; Di Molfetta, G.; Brachet, M.; Debbasch, F. |
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Title |
Quantum walks and non-Abelian discrete gauge theory |
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 |
1 |
Pages |
012335 - 6pp |
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Abstract |
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1) Maxwell fields and SU(N) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs. |
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Address |
[Arnault, Pablo; Debbasch, Fabrice] Univ Paris 06, Univ Paris 04, PSL Res Univ, LERMA,Observ Paris,CNRS,UMR 8112, F-75014 Paris, France, Email: pablo.arnault@upmc.fr; |
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Amer Physical Soc |
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English |
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ISSN |
2469-9926 |
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Conference |
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Notes |
WOS:000380095000005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2761 |
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Author |
Arnault, P.; Macquet, A.; Angles-Castillo, A.; Marquez-Martin, I.; Pina-Canelles, V.; Perez, A.; Di Molfetta, G.; Arrighi, P.; Debbasch, F. |
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Title |
Quantum simulation of quantum relativistic diffusion via quantum walks |
Type |
Journal Article |
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Year |
2020 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
53 |
Issue |
20 |
Pages |
205303 - 39pp |
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Keywords |
noisy quantum walks; noisy quantum systems; decoherence; Lindblad equation; quantum simulation; relativistic diffusions; telegraph equation |
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Abstract |
Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position. |
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Address |
[Arnault, Pablo; Angles-Castillo, Andreu; Marquez-Martin, Ivan; Pina-Canelles, Vicente; Perez, Armando; Di Molfetta, Giuseppe] Univ Valencia, Dept Fis Teor, Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ic.uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Conference |
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Notes |
WOS:000531359000001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4390 |
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Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
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Title |
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks |
Type |
Journal Article |
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Year |
2019 |
Publication |
Scientific Reports |
Abbreviated Journal |
Sci Rep |
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Volume |
9 |
Issue |
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Pages |
10904 - 10pp |
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Abstract |
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices. |
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Address |
[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Univ Toulon & Var, Aix Marseille Univ, CNRS, LIS, Marseille, France, Email: pablo.arrighi@univ-amu.fr; |
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Publisher |
Nature Publishing Group |
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English |
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Edition |
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ISSN |
2045-2322 |
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Notes |
WOS:000477701800007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4081 |
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Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
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Title |
Dirac equation as a quantum walk over the honeycomb and triangular lattices |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
97 |
Issue |
6 |
Pages |
062111 - 5pp |
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Keywords |
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Abstract |
A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2 + 1) dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces. |
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Address |
[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Aix Marseille Univ, Univ Toulon, LIS, CNRS, Marseille, France, Email: pablo.arrighi@univ-amu.fr; |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series 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 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000435076800001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3624 |
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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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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series 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 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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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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