Top

Quantum Information Processing

Published in:

01-02-2021

Continuous time limit of the DTQW in 2D+1 and plasticity

Authors: Michael Manighalam, Giuseppe Di Molfetta

Published in: Quantum Information Processing | Issue 2/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A Plastic quantum walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in Di Molfetta and Arrighi (Quant Inf Process 19(2): 47, 2020), leading to a general quantum simulation scheme for simulating fermions in the relativistic and non-relativistic regimes. The extension to two physical dimensions is still missing and here, as a novel result, we demonstrate necessary and sufficient conditions concerning which discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. We consider coin operators as general 4 parameter unitary matrices, with parameters which are functions of the lattice step size \(\varepsilon \). This dependence on \(\varepsilon \) encapsulates all functions of \(\varepsilon \) for which a Taylor series expansion in \(\varepsilon \) is well defined, making our results very general.

previous article Locally distinguishing multipartite orthogonal product states with different entanglement resource

next article Quantifying environmental memory degree from the aspect of environmental sensitivity

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

This constraint reduces to the constraint obtained for \(\theta _{0}\) in Ref. [19] when the 1D limit is taken, i.e., \(\zeta _{0y},\theta _{0y},\phi _{0y},\delta =0\) (see Eq. (A7) of Ref. [19])

Di Molfetta, G., Arrighi, P.: A quantum walk with both a continuous-time limit and a continuous-spacetime limit. Quant. Inf. Process. 19(2), 47 (2020)ADSMathSciNetCrossRef

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

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

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

Strauch, F.W.: Connecting the discrete-and continuous-time quantum walks. Phys. Rev. A 74(3), 030301 (2006)ADSMathSciNetCrossRef

Arnault, P., Debbasch, F.: Quantum walks and gravitational waves. Ann. Phys. 383, 645–661 (2017). https://doi.org/10.1016/j.aop.2017.04.003ADSMathSciNetCrossRefMATH

Di Molfetta, G., Debbasch, F.: Discrete-time quantum walks: continuous limit and symmetries. J. Math. Phys. 53(12), 123302 (2012)ADSMathSciNetCrossRef

Di Molfetta, G., Brachet, M., Debbasch, F.: Quantum Walks in artificial electric and gravitational Fields. Phys. A Stat. Mech. Appl. 397, 157 (2014)MathSciNetCrossRef

Arnault, P., Debbasch, F.: Quantum walks and discrete gauge theories. Phys. Rev. A (2016). https://doi.org/10.1103/physreva.93.052301CrossRefMATH

10.

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

11.

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

12.

Arnault, P., Debbasch, F.: Landau levels for discrete-time quantum walks in artificial magnetic fields. Phys. A Stat. Mech. Appl. 443, 179 (2016). https://doi.org/10.1016/j.physa.2015.08.011 URL http://www.sciencedirect.com/science/article/pii/S0378437115006664

13.

Di Molfetta, G., Brachet, M., Debbasch, F.: Quantum walks as massless Dirac fermions in curved space-time. Phys. Rev. A 88(4), 042301 (2013)ADSCrossRef

14.

Arrighi, P., Facchini, F.: Quantum walking in curved spacetime: (3+1) dimensions, and beyond. Quant. Inf. Comput. 17(9-10), 0810 (2017). URL https://arxiv.org/abs/1609.00305. ArXiv:1609.00305

15.

Succi, S., Fillion-Gourdeau, F., Palpacelli, S.: Quantum Lattice Boltzmann is a quantum walk. EPJ Quant. Technol. (2015). https://doi.org/10.1140/epjqt/s40507-015-0025-1CrossRef

16.

Arrighi, P., Di Molfetta, G., Márquez-Martín, I., Pérez, A.: From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular quantum walks. Sci. Rep. 9(1), 1 (2019)CrossRef

17.

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

18.

Zohar, E., Burrello, M.: Formulation of lattice gauge theories for quantum simulations. Phys. Rev. D 91(5), 054506 (2015)ADSMathSciNetCrossRef

19.

Manighalam, M., Kon, M.: Continuum limits of the 1D discrete time quantum walk (2019)

Title: Continuous time limit of the DTQW in 2D+1 and plasticity
Authors: Michael Manighalam
Giuseppe Di Molfetta
Publication date: 01-02-2021
Publisher: Springer US
Published in: Quantum Information Processing / Issue 2/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-021-03011-5

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 2/2021

Nonlinear steering criteria for arbitrary two-qubit quantum systems

Models in quantum computing: a systematic review

Controllable and shortcut-based population transfers with a composite system of a nitrogen-vacancy electron spin and microwave photons

Differential phase encoded measurement-device-independent quantum key distribution

A note on “new quantum key agreement protocols based on Bell states”

Partitions of correlated N-qubit systems