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Quantum Information Processing

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01.03.2020

A quantum cellular automaton for one-dimensional QED

verfasst von: Pablo Arrighi, Cédric Bény, Terry Farrelly

Erschienen in: Quantum Information Processing | Ausgabe 3/2020

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Abstract

We propose a discrete spacetime formulation of quantum electrodynamics in one dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a “convergent” sequence of quantum cellular automata, parameterized by the spacetime lattice spacing—encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics.

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Ahlbrecht, A., Alberti, A., Meschede, D., Scholz, V.B., Werner, A.H., Werner, R.F.: Molecular binding in interacting quantum walks. New J. Phys. 14(7), 073050 (2012)ADSCrossRef

Ambjørn, J., Jurkiewicz, J., Loll, R.: Emergence of a 4d world from causal quantum gravity. Phys. Rev. Lett. 93(13), 131301 (2004)ADSMathSciNetCrossRef

Arnault, P., Debbasch, F.: Quantum walks and gravitational waves. arXiv preprint arXiv:1609.00722 (2016)

Arnault, P., Molfetta, G.D., Brachet, M., Debbasch, F.: Quantum walks and non-abelian discrete gauge theory. Phys. Rev. A 94(1), 012335 (2016)ADSMathSciNetCrossRef

Arrighi, P., Facchini, S.: Quantum walking in curved spacetime: \((3+1)\)-dimensions, and beyond. Pre-print arXiv:1609.00305 (2016)

Arrighi, P., Forets, M., Nesme, V.: The dirac equation as a quantum walk: higher-dimensions, convergence. Pre-print arXiv:1307.3524 (2013)

Arrighi, P., Grattage, J.: A quantum game of life. In second symposium on cellular automata Journées Automates Cellulaires (JAC 2010), Turku, December 2010. TUCS Lecture Notes 13, pp. 31–42 (2010)

Arrighi, P., Molfetta, G.D., Eon, N.: A gauge-invariant reversible cellular automaton. In: International Workshop on Cellular Automata and Discrete Complex Systems, pp. 1–12. Springer (2018)

Arrighi, P., Nesme, V., Werner, R.: Unitarity plus causality implies localizability. J. Comput. Syst. Sci. 77, 372–378 (2010). QIP 2010 (long talk)

10.

Arrighi, P., Grattage, J.: Partitioned quantum cellular automata are intrinsically universal. Nat. Comput. 11, 13–22 (2012)MathSciNetCrossRef

11.

Arrighi, P., Patricot, C.: A note on the correspondence between qubit quantum operations and special relativity. J. Phys. A: Math. Gen. 36(20), L287–L296 (2003)ADSMathSciNetCrossRef

12.

Arrighi, P., Facchini, S., Forets, M.: Discrete lorentz covariance for quantum walks and quantum cellular automata. New J. Phys. 16(9), 093007 (2014)MathSciNetCrossRef

13.

Arrighi, P., Nesme, V., Forets, M.: The dirac equation as a quantum walk: higher dimensions, observational convergence. J. Phys. A: Math. Theor. 47(46), 465302 (2014)ADSMathSciNetCrossRef

14.

Arrighi, P., Facchini, S., Forets, M.: Quantum walking in curved spacetime. Quant. Inf. Process. 15, 3467–3486 (2016)ADSMathSciNetCrossRef

15.

Bialynicki-Birula, I., Weyl, D.: Maxwell equations on a lattice as unitary cellular automata. Phys. Rev. D. 49(12), 6920–6927 (1994)ADSMathSciNetCrossRef

16.

Bibeau-Delisle, A., Bisio, A., D’Ariano, G.M., Perinotti, P., Tosini, A.: Doubly special relativity from quantum cellular automata. EPL (Europhysics Letters) 109(5), 50003 (2015)ADSCrossRef

17.

Bisio, A., D’Ariano, G.M., Perinotti, P.: Quantum walks, weyl equation and the lorentz group. Found. Phys. 47(8), 1065–1076 (2017)ADSMathSciNetCrossRef

18.

Bisio, A., D’Ariano, G.M., Perinotti, P., Tosini, A.: Thirring quantum cellular automaton. Phys. Rev. A 97(3), 032132 (2018)ADSCrossRef

19.

Cedzich, C., Geib, T., Werner, A.H., Werner, R.F.: Quantum walks in external gauge fields. arXiv:1808.10850v1 (2018)

20.

Debbasch, F: Action principles for quantum automata and lorentz invariance of discrete time quantum walks. arXiv preprint arXiv:1806.02313 (2018)

21.

DeGrand, T., DeTar, C.: Lattice Methods for Quantum Chromodynamics. World Scientific, Singapore (2006)CrossRef

22.

Destri, C., de Vega, H.J.: Light cone lattice approach to fermionic theories in 2-d: the massive Thirring model. Nucl. Phys. B 290, 363 (1987)ADSMathSciNetCrossRef

23.

Eisert, J., Gross, D.: Supersonic quantum communication. Phys. Rev. Lett. 102(24), 240501 (2009)ADSCrossRef

24.

Ercolessi, E., Facchi, P., Magnifico, G., Pascazio, S., Pepe, F.V.: Phase transitions in \({Z}_{n}\) gauge models: Towards quantum simulations of the schwinger-weyl qed. Phys. Rev. D 98, 074503 (2018)ADSMathSciNetCrossRef

25.

Farrelly, T.C.: Insights from Quantum Information into Fundamental Physics. PhD thesis, University of Cambridge, 2015. arXiv:1708.08897 (2015)

26.

Farrelly, T.C., Short, A.J.: Causal fermions in discrete space-time. Phys. Rev. A 89(1), 012302 (2014)ADSCrossRef

27.

Feynman, H.: Quantum mechanics and path integrals. McGraw-Hill. Feynman relativistic chessboard (1965)

28.

Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6), 467–488 (1982)MathSciNetCrossRef

29.

Feynman, R.P.: Quantum mechanical computers. Found. Phys. 16(6), 507–531 (1986)ADSMathSciNetCrossRef

30.

Fillion-Gourdeau, F., MacLean, S., Laflamme, R.: Algorithm for the solution of the dirac equation on digital quantum computers. Phys. Rev. A 95, 042343 (2017)ADSCrossRef

31.

Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86(1), 153 (2014)ADSCrossRef

32.

Hastings, W.K.: Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1), 97–109 (1970)MathSciNetCrossRef

33.

Jordan, S.P., Lee, K.S.M., Preskill, J.: Quantum algorithms for fermionic quantum field theories. arXiv:1404.7115v1 (2014)

34.

Jordan, S.P., Lee, K.S.M., Preskill, J.: Quantum algorithms for quantum field theories. Science 336(6085), 1130–1133 (2012)ADSCrossRef

35.

Kaplan, D.B.: Chiral symmetry and lattice fermions. arXiv:0912.2560v2 (2009)

36.

Klco, N., Dumitrescu, E.F., McCaskey, A.J., Morris, T.D., Pooser, R.C., Sanz, M., Solano, E., Lougovski, P., Savage, M.J.: Quantum-classical computation of schwinger model dynamics using quantum computers. Phys. Rev. A 98, 032331 (2018)ADSCrossRef

37.

38.

Kogut, J., Susskind, L.: Hamiltonian formulation of wilson’s lattice gauge theories. Phys. Rev. D 11(2), 395 (1975)ADSCrossRef

39.

Martinez, E.A., Muschik, C.A., Schindler, P., Nigg, D., Erhard, A., Heyl, M., Hauke, P., Dalmonte, M., Monz, T., Zoller, P., et al.: Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534(7608), 516–519 (2016)ADSCrossRef

40.

Melnikov, K., Weinstein, M.: Lattice schwinger model: confinement, anomalies, chiral fermions, and all that. Phys. Rev. D 62(9), 094504 (2000)ADSCrossRef

41.

Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85(5–6), 551–574 (1996)

42.

Molfetta, G.D., Pérez, A.: Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys. 18(10), 103038 (2016)CrossRef

43.

Molfetta, G.D., Brachet, M., Debbasch, F.: Quantum walks in artificial electric and gravitational fields. Physica A 397, 157–168 (2014) ADSMathSciNetCrossRef

44.

Nielsen, H.B., Ninomiya, M.: A no-go theorem for regularizing chiral fermions. Phys. Lett. B 105(2–3), 219–223 (1981)ADSCrossRef

45.

Osborne, T.J.: Continuum limits of quantum lattice systems. arXiv:1901.06124v1 (2019)

46.

Park, S.T.: Propagation of a relativistic electron wave packet in the dirac equation. Phys. Rev. A 86(6), 062105 (2012)ADSCrossRef

47.

Quigg, C.: Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. Princeton University Press, Princeton (2013)CrossRef

48.

Rico, E., Pichler, T., Dalmonte, M., Zoller, P., Montangero, S.: Tensor networks for lattice gauge theories and atomic quantum simulation. Phys. Rev. Lett. 112(20), 201601 (2014)ADSCrossRef

49.

Rovelli, C.: Simple model for quantum general relativity from loop quantum gravity. J. Phys. 314, 012006 (2011)

50.

Schumacher, B., Werner, R.: Reversible quantum cellular automata. arXiv pre-print quant-ph/0405174, (2004)

51.

Silvi, P.: Rico, enrique, calarco, tommaso, montangero, simone: lattice gauge tensor networks. New J. Phys. 16(10), 103015 (2014)ADSMathSciNetCrossRef

52.

Succi, S., Benzi, R.: Lattice Boltzmann equation for quantum mechanics. Physica D 69(3), 327–332 (1993)ADSMathSciNetCrossRef

53.

Zohar, E., Cirac, J.I., Reznik, B.: Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices. Rep. Prog. Phys. 79(1), 014401 (2015)ADSMathSciNetCrossRef

Titel: A quantum cellular automaton for one-dimensional QED
verfasst von: Pablo Arrighi
Cédric Bény
Terry Farrelly
Publikationsdatum: 01.03.2020
Verlag: Springer US
Erschienen in: Quantum Information Processing / Ausgabe 3/2020
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-019-2555-4

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