Skip to main content
Log in

Analog quantum computing (AQC) and the need for time-symmetric physics

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper discusses what will be necessary to achieve the full potential capabilities of analog quantum computing (AQC), which is defined here as the enrichment of continuous-variable computing to include stochastic, nonunitary circuit elements such as dissipative spin gates and address the wider range of tasks emerging from new trends in engineering, such as approximation of stochastic maps, ghost imaging and new forms of neural networks and intelligent control. This paper focuses especially on what is needed in terms of new experiments to validate remarkable new results in the modeling of triple entanglement, and in creating a pathway which links fundamental theoretical work with hard core experimental work, on a pathway to AQC similar to the pathway to digital quantum computing already blazed by Zeilinger’s group. It discusses the most recent experiments and reviews two families of alternative models based on the traditional eigenvector projection model of polarizers and on a new family of local realistic models based on Markov Random Fields across space–time adhering to the rules of time-symmetric physics. For both families, it reviews lumped parameter versions, continuous time extension and possibilities for extension to continuous space and time.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci. 400(1818), 97–117 (1985)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Barron, Andrew R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inf. Theory 39(3), 930–945 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lloyd, S., Braunstein, S.L.: Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784–1787 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  4. Kendon, V.M., Nemoto, K., Munro, W.J.: Quantum analogue computing. Philos. Trans. R. Soc. A 368, 3609–3620 (2010)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Siegelmann, H.T., Sontag, E.D.: On the computational power of neural nets. J. Comput. Syst. Sci. 50(1), 132–150 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ezhov, A.A., Berman, G.P.: Introduction to Quantum Neural Technologies. Rinton Press, Princeton (2003)

    MATH  Google Scholar 

  7. Santoro, G.E., Tosatti, E.: Optimization using quantum mechanics: quantum annealing through adiabatic evolution. J. Phys. A 39, R393 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. Werbos, P.J.: RLADP—foundations, common misconceptions, and the challenges ahead. In: Lewis, Frank L., Liu, D. (eds.) Reinforcement Learning and Approximate Dynamic Programming for Feedback Control. Wiley, Hoboken (2012)

    Google Scholar 

  9. Werbos, P.J.: Approximate dynamic programming for real-time control and neural modeling. In: White, D., Sofge, D. (eds.) Handbook of Intelligent Control. Van Nostrand, New York (1992)

    Google Scholar 

  10. Werbos, P.J.: How can we ever understand how the brain works? In: Kozma, R., Freeman, W.J. (eds.) Cognitive Phase Transitions in the Cerebral Cortex—Enhancing the Neuron Doctrine by Modeling Neural Fields, Springer Series: Studies in Systems, Decision and Control. Springer International Publ. AG, Cham (2015)

    Google Scholar 

  11. Werbos, P.J.: Intelligence in the brain: a theory of how it works and how to build it. Neural Netw. 22(3), 200–212 (2009)

    Article  Google Scholar 

  12. Bennett, C.H., Landauer, R.: The fundamental physical limits of computation. Sci. Am. 253(1), 48–56 (1985)

    Article  ADS  Google Scholar 

  13. Bouwmeester, D., Pan, J.W., Daniel, M., Weinfurter, H., Zeilinger, A.: Observation of three-photon. Phys. Rev. Lett. 82, 1345 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. Werbos, P.: How to use memristors for more than just memory: how to use learning to expand applications. In: Kozma, R., Pino, R., Pazienza, G. (eds.) Advances in Neuromorphic Memristor Science and Applications. Springer, New York (2012)

    Google Scholar 

  15. Werbos, P.J.: From ADP to the brain: foundations, roadmap, challenges and research priorities. In: Proceedings of the International Joint Conference on Neural Networks. IEEE, Beijing (2014)

  16. Werbos, P.J.: Bell’s theorem, many worlds and backwards-time physics: not just a matter of interpretation. Int. J. Theor. Phys. 47(11), 2862–2874 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Walls, D.F., Gerard, J.M.: Quantum Optics. Springer, New York (2007)

    MATH  Google Scholar 

  18. Carmichael, H.: Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  19. Werbos, P.J.: Example of lumped parameter modeling of a quantum optics circuit. In: SPIE Proceedings of Quantum Information and Computation XII, SPIE 9123-10 (2014)

  20. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  21. Gershenfeld, N.A., Chuang, I.L.: Bulk spin-resonance quantum computation. Science 275(5298), 350–356 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464(7285), 45–53 (2010)

    Article  ADS  Google Scholar 

  23. Pittman, T.B., Shih, Y.H., Strekalov, D.V., Sergienko, A.V.: Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A 52(5), R3429 (1995)

    Article  ADS  Google Scholar 

  24. Awschalom, D.D. (ed.): Spin Electronics. Springer, New York (2004)

    Google Scholar 

  25. Bose, R., Sridharan, D., Kim, H., Solomon, G.S., Waks, E.: Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity. Phys. Rev. Lett. 108, 227402 (2012)

    Article  ADS  Google Scholar 

  26. Darankur, B., Verma, P.K.: The braided single-stage protocol for quantum-secure communication. In: SPIE Proceedings Quantum Information and Computation XII (2014)

  27. Lai, H., Orgun, M., Xue, L., Xiao, J., Pieprzyk, J.: Dual compressible hybrid quantum secret sharing schenes based on extended unitary operation. In: SPIE Proceedings of Quantum Information and Computation XII (2014)

  28. National Science Foundation: New lower-cost technology to produce many entangled photons and test their properties, ECCS1444491. http://www.nsf.gov/awardsearch/showAward?AWD_ID=1444491 (2014). Accessed 29 Sept 2015

  29. Peng, T., Shih, Y.: Simulation of Bell and GHZ states with thermal fields. In: Scully, M. (ed.) Princeton-TAMU Workshop on Classical-Quantum Interface, Princeton, May 27–29 (2015)

  30. Werbos, P. J.: Time-symmetric physics: a radical approach to the decoherence problem. In: Steck, J., Behrman, E. (eds.) Proceedings of the workshop on Quantum Computing of the conference Pacific Rim Artificial Intelligence (PIRCAI) (2014). Also posted at arXiv:1501.00027 with links to audio and slides

  31. Werbos, P.J.: Extension of the Glauber–Sudarshan mapping for classical and quantum energy spectra. Int. IFNA-ANS J. Probl. Nonlinear Anal. Eng. Syst. 20, 1–10 (2014)

  32. Werbos,P.J.: Local realistic model of Bell Theorem experiment and alternative model of quantum measurement. arXiv:1403.0469

  33. Werbos, P.J.: Stochastic path model of polaroid polarizer for Bell’s Theorem and triphoton experiments. Int. J. Bifurc. Chaos 25(3), 1550046 (2015)

    Article  MathSciNet  Google Scholar 

  34. Peng, T., et al.: Delayed-choice quantum eraser with thermal light. Phys. Rev. Lett. 112(18), 180401 (2014)

    Article  ADS  Google Scholar 

  35. Strekalov, D.V., Erkmen, B.I., Yu, N.: Ghost imaging of space objects. J. Phys. Conf. Ser. 414(1). IOP Publishing. http://iopscience.iop.org/1742-6596/414/1/012037/pdf/1742-6596_414_1_012037.pdf (2013)

  36. Carmichael, H.J.: Statistical Methods in Quantum Optics 2: Non-classical Fields. Springer, New York (2009)

    Google Scholar 

  37. Box, G.E.P., Jenkins, G.M.: Time Series Analysis: Forecasting and Control, Revised Ed. Holden-Day, San Francisco (1976)

    MATH  Google Scholar 

  38. El-Karoui, N., Mazliak, L. (eds.): Backward Stochastic Differential Equations. Addison-Wesley Longman, Boston (1997)

    MATH  Google Scholar 

  39. Clauser, J.F., Shimony, A.: Bell’s theorem. Experimental tests and implications. Rep. Prog. Phys. 41(12), 1881–1927 (1978)

    Article  ADS  Google Scholar 

  40. Datta, S.: Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28(4), 253–278 (2000)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paul J. Werbos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Werbos, P.J., Dolmatova, L. Analog quantum computing (AQC) and the need for time-symmetric physics. Quantum Inf Process 15, 1273–1287 (2016). https://doi.org/10.1007/s11128-015-1146-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1146-2

Keywords

Navigation