Quantum walking in curved spacetime: discrete metric

Pablo Arrighi; Giuseppe Di Molfetta; Stefano Facchini

doi:10.22331/q-2018-08-22-84

Quantum walking in curved spacetime: discrete metric

Pablo Arrighi¹, Giuseppe Di Molfetta², and Stefano Facchini³

¹Aix-Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, and IXXI, Lyon, France
²Aix-Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France and Departamento de Física Teórica and IFIC, Universidad de Valencia-CSIC, Dr. Moliner 50, 46100-Burjassot, Spain
³Aix-Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France

Published:	2018-08-22, volume 2, page 84
Eprint:	arXiv:1711.04662v4
Doi:	https://doi.org/10.22331/q-2018-08-22-84
Citation:	Quantum 2, 84 (2018).

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Abstract

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.

► BibTeX data

@article{Arrighi2018quantumwalkingin,
  doi = {10.22331/q-2018-08-22-84},
  url = {https://doi.org/10.22331/q-2018-08-22-84},
  title = {Quantum walking in curved spacetime: discrete metric},
  author = {Arrighi, Pablo and Molfetta, Giuseppe Di and Facchini, Stefano},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {84},
  month = aug,
  year = {2018}
}

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[6] Pablo Arnault, Armando Pérez, Pablo Arrighi, and Terry Farrelly, "Discrete-time quantum walks as fermions of lattice gauge theory", Physical Review A 99 3, 032110 (2019).

[7] Marcelo A. Pires, Giuseppe Di Molfetta, and Sílvio M. Duarte Queirós, "Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps", Scientific Reports 9 1, 19292 (2019).

[8] Arindam Mallick, Sanjoy Mandal, Anirban Karan, and C M Chandrashekar, "Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk", Journal of Physics Communications 3 1, 015012 (2019).

[9] Arindam Mallick, Sanjoy Mandal, Anirban Karan, and C. M. Chandrashekar, "Simulating Dirac Hamiltonian in Curved Space-time by Split-step Quantum Walk", arXiv:1712.03911, (2017).

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