Skip to main content
SpringerLink
Log in

Quantum Systems Simulatability Through Classical Networks

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

A Correction to this article was published on 27 January 2023

This article has been updated

Abstract

We have shown that any two quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. These transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum system. Different quantum systems are connected in such a way that studying one of them allows understanding the other. This result can be applied to the field of simulation of quantum systems, in order to mimic more complicated quantum systems from another simulatable quantum system. Given that there is a bridge that allows to simulate a particular quantum system on these kind of Hilbert spaces using classical circuits we will provide a general scenario to extend this bridge to simulate the time evolution, via Schrödinger equation, of any of these quantum systems using classical circuits. This classical systems can be implemented and controlled more easily in the laboratory than the quantum systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Change history

References

  1. Feynman, R.P.: Simulation physics with computers. Int. J. Theor. Phys. 21, 467 (1982)

    Article  Google Scholar 

  2. Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014)

    Article  ADS  Google Scholar 

  3. Lloyd, S.: Universal quantum simulators. Science 273(5278), 1073–1078 (1996)

    Article  ADS  MATH  Google Scholar 

  4. Lamata, L., Parra-Rodriguez, A., Sanz, M., Solano, E.: Digital-analog quantum simulations with superconducting circuits. Adv. in Phys. X 3, 1457981 (2018)

    ADS  Google Scholar 

  5. Caruso, M., Fanchiotti, H., García Canal, C.A.: Equivalence between classical and quantum dynamics. Neutral kaons and electric circuits. Ann. Phys. 326(10), 2717–2736 (2011)

    Article  ADS  MATH  Google Scholar 

  6. Caruso, M., Fanchiotti, H., García Canal, C.A., Mayosky, M., Veiga, A: The quantum CP-violating kaon system reproduced in the electronic laboratory. Proc. R. Soc. A. 472, 20160615 (2016)

    Article  ADS  MATH  Google Scholar 

  7. Varadarajan, V.S.: Formal reduction theory of meromorphic differential equations: A group theoretic view. Pac. J. Math. 109(1), 1–80 (1986)

    Google Scholar 

  8. Varadarajan, V.S.: Linear meromorphic differential equations: A modern point of view. Am. Math. Soc. 33, 1–42 (1996)

    Article  MATH  Google Scholar 

  9. Varadarajan, V.S.: Vector bundles and connections in physics and mathematics: Some historical remarks. Trends Math, 502–541 (2003)

  10. Mostafazadeh, A.: Quantum canonical transformations and exact solution of the Schrödinger equation. J. Math. Phys. 38, 3489–3496 (1997)

    Article  ADS  MATH  Google Scholar 

  11. Mostafazadeh, A.: Time dependent diffeomorphisms as quantum canonical transformations and the time dependent harmonic oscillator. J. Phys. A 31, 6495–6503 (1998)

    Article  ADS  MATH  Google Scholar 

  12. Mostafazadeh, A.: Geometric phases, symmetries of dynamical invariants, and exact solution of the Schrodinger equation. J. Phys. A 34, 6325–6338 (2001)

    Article  ADS  MATH  Google Scholar 

  13. Magnus, W: On the exponential solution of differential equations for a linear operator. Comm. Pure Appl. Math. VII(4), 649–673 (1954)

    Article  MATH  Google Scholar 

  14. Giles, B., Selinger, P.: Exact synthesis of multiqubit Clifford+T circuits. Phys. Rev. A 87, 032332 (2013)

    Article  ADS  Google Scholar 

  15. Rosner, J.L.: . Am. J. Phys. 64(8), 982–985 (1996)

    Article  ADS  Google Scholar 

  16. Arnold, V.I.: Ordinary differential equations. Springer (1992)

  17. Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations. Springer (1980)

  18. Balabanian, N., Bickart, T.A.T.A.: Linear Network Theory: Analysis, Properties, Design and Synthesis. Wiley (1969)

  19. Carlin, H., Giordano, A.: Network Theory: An Introduction to Reciprocal and Nonreciprocal Circuits. Prentice Hall (1964)

Download references

Acknowledgments

We thank to FIDESOL for the support and recall also the anonymous readers for their constructive criticism to this work.

Author information

Authors and Affiliations

  1. Fundación I+D del Software Libre, FIDESOL, Granada, (18100), España

    M. Caruso

  2. Campus de Fuentenueva, Universidad de Granada, Granada, (18071), España

    M. Caruso

Authors
  1. M. Caruso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Caruso.

Ethics declarations

Conflict of Interests

The author declares that there are no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Caruso, M. Quantum Systems Simulatability Through Classical Networks. Int J Theor Phys 61, 30 (2022). https://doi.org/10.1007/s10773-022-05045-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05045-6

Keywords

Search

Navigation