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Quantum computing algorithm for electromagnetic field simulation

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Abstract

Quantum computing offers new concepts for the simulation of complex physical systems. A quantum computing algorithm for electromagnetic field simulation is presented here. The electromagnetic field simulation is performed on the basis of the Transmission Line Matrix (TLM) method. The Hilbert space formulation of TLM allows us to obtain a time evolution operator for the TLM method, which can then be interpreted as the time evolution operator of a quantum system, thus yielding a quantum computing algorithm. Further, the quantum simulation is done within the framework of the quantum circuit model of computation. Our aim has been to address the design problem in electromagnetics—given an initial condition and a final field distribution, find the structures which satisfy these. Quantum computing offers us the possibility to solve this problem from first principles. Using quantum parallelism we simulate a large number of electromagnetic structures in parallel in time and then try to filter out the ones which have the required field distribution.

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References

  1. Abrams, D., Lloyd, S.: Nonlinear quantum mechanics implies Polynomial-Time solution for NP-Complete and #P problems. Phys. Rev. Lett. 81(18), 3992 (1998). doi:10.1103/PhysRevLett.81.3992. http://link.aps.org/abstract/PRL/v81/p3992. Copyright (C) 2009 The American Physical Society; Please report any problems to prola@aps.org

  2. Averin, D.: Quantum computing and quantum measurement with mesoscopic Josephson junctions. Fortschritte der Physik 48(9–11), 1055–1074 (2000). http://dx.doi.org/10.1002/1521-3978(200009)48:9/11<1055::AID-PROP1055>3.0.CO;2-1

  3. Barenco A.: Quantum physics and computers. Contem. Phys. 37(5), 375–389 (1996)

    Article  CAS  ADS  Google Scholar 

  4. Barenco A., Ekert A., Suominen K., Torma P.: Approximate quantum Fourier transform and decoherence. SIAM J. Comput. Phys. Rev. A 54, 139 (1994)

    MathSciNet  ADS  Google Scholar 

  5. Berggren K.: Quantum computing with superconductors. Proc. IEEE 92(10), 1630–1638 (2004)

    Article  Google Scholar 

  6. Berman G.P., Ezhov A.A., Kamenev D.I., Yepez J.: Simulation of the diffusion equation on a type-II quantum computer. Phys. Rev. A 66(1), 12,310 (2002)

    Article  Google Scholar 

  7. Childs, A., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., Spielman, D.: Exponential algorithmic speedup by quantum walk. quant-ph/0209131 (2002). doi:10.1145/780542.780552. http://arxiv.org/abs/quant-ph/0209131. Proceedings of the 35th ACM Symposium on Theory of Computing (STOC 2003), pp. 59–68

  8. Christopoulos C.: The Transmission Line Modeling Method TLM. IEEE Press, New York (1995)

    Book  Google Scholar 

  9. Christopoulos, C., Russer, P.: Application of TLM to EMC problems. In: Uzunoglu, N., Kaklamani, D.I., Nikita, K.S. (eds.) Applied Computational Electromagnetics, NATO ASI Series, pp. 324–350. Springer, Berlin (2000)

  10. Christopoulos, C., Russer, P.: Application of TLM to microwave circuits. In: Uzunoglu, N., Kaklamani, D.I., Nikita, K.S. (eds.) Applied Computational Electromagnetics, NATO ASI Series, pp. 300–323. Springer, Berlin (2000)

  11. Coppersmith, D.: An approximate Fourier transform useful in quantum factoring. Arxiv preprint quant-ph/0201067 (2002)

  12. Deutsch D.: Quantum theory, the church-turing principle and the universal quantum number. Proc. Roy. Soc. Lon. A 400, 97–117 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. DiVincenzo, D.: Quantum computation. Science 270(5234), 255–261 (1995). doi:10.1126/science.270.5234.255. http://www.sciencemag.org/cgi/content/abstract/270/5234/255

    Google Scholar 

  14. Ekert, A., Jozsa, R., Marcer, P.: Quantum algorithms: Entanglement-Enhanced information processing [and discussion]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, pp. 1769–1782 (1998)

  15. Feynman, R.: Simulating physics with computers. Int. J. Theore. Phys. 21(6), 467–488 (1982). doi:10.1007/BF02650179. http://dx.doi.org/10.1007/BF02650179

    Google Scholar 

  16. Freiser M., Marcus P.: A survey of some physical limitations on computer elements. IEEE Trans. Magn. 5(2), 82–90 (1969)

    Article  ADS  Google Scholar 

  17. Grover, L.K.: Quantum computers can search arbitrarily large databases by a single query. Phys. Rev. Lett. 79(23), 4709 (1997). doi:10.1103/PhysRevLett.79.4709. http://link.aps.org/abstract/PRL/v79/p4709. Copyright (C) 2009 The American Physical Society; Please report any problems to prola@aps.org

    Google Scholar 

  18. Grover, L.K.: Quantum computing: beyond factorization and search. Science 281(5378), 792–794 (1998). doi:10.1126/science.281.5378.792. http://www.sciencemag.org

    Google Scholar 

  19. Hoefer W.J.: The transmission line matrix method-theory and applications. IEEE. Trans. Microw. Theory. Tech. 33, 882–893 (1985)

    Article  ADS  Google Scholar 

  20. Knill E.: Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005)

    Article  CAS  PubMed  ADS  Google Scholar 

  21. Krumpholz M., Russer P.: A field theoretical derivation TLM. IEEE. Trans. Microw. Theory. Tech. 42, 1660–1668 (1994)

    Article  ADS  Google Scholar 

  22. Krumpholz M., Russer P.: Two dimensional FDTD and TLM. Int. J. Numeri. Modell. 7, 141–153 (1994)

    Article  MathSciNet  Google Scholar 

  23. Lloyd, S.: Universal quantum simulators. Science 273(5278), 1073–1078 (1996). doi:10.1126/science.273.5278.1073. http://www.sciencemag.org/cgi/content/abstract/273/5278/1073

    Google Scholar 

  24. Marinescu D.C., Marinescu G.M.: Lectures on Quantum Computing. Computer Science Department, University of Central Florida, Florida (2003)

    Google Scholar 

  25. Meyer D.A.: Quantum computing classical physics. Philos. Trans. R. Soc. Lond. A 360, 395–405 (2002)

    Article  MATH  ADS  Google Scholar 

  26. Nielssen M.A., Chuang I.L.: Quantum Computation and Quantum Information. 1st edn. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  27. Pravia M.A., Chen Z., Yepez J., Cory D.G.: Experimental demonstration of quantum lattice gas computation. Quantum Inf. Process. 2(1), 97–116 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  28. Russer P.: Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering. 2nd edn. Artech House, Boston (2006)

    Google Scholar 

  29. Russer P., Krumpholz M.: The Hilbert space formulation of the TLM method. Int. J. Numeri. Modell. 6, 29–45 (1993)

    Article  MathSciNet  Google Scholar 

  30. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science, 20–22 Nov. 1994, pp. 124–134 (1994)

  31. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. pp. 303–332 (1999)

  32. Steane A.: Quantum computing. Rep. Prog. Phys. 61, 117–173 (1998)

    Article  CAS  MathSciNet  ADS  Google Scholar 

  33. Taylor, J., Lukin, M.: Dephasing of quantum bits by a Quasi-Static mesoscopic environment. Quantum Inf. Process. 5(6), 503–536 (2006). doi:10.1007/s11128-006-0036-z. http://dx.doi.org/10.1007/s11128-006-0036-z

  34. Yepez J.: Lattice-gas quantum computation. Int. J. Modern Phys. C-Phys. Comp. 9(8), 1587–1596 (1998)

    Article  ADS  Google Scholar 

  35. Yepez, J.: Quantum computation of fluid dynamics, Lecture Notes in Computer Science, vol. 1509, pp. 34–60. Springer, Heidelberg (1999). doi:10.1007/3-540-49208-9-3

  36. Yepez, J.: Quantum lattice-gas model for computational fluid dynamics. Phys. Rev. E 63(4), 46,702/ 1–18 (2001)

    Google Scholar 

  37. Yepez J.: Quantum lattice-gas model for the diffusion equation. Int. J. Modern Phys. C-Phys. Comp. 12(9), 1285–1304 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  38. Yepez J.: Type-II quantum computers. Int. J. Modern Phy. C-Phys. Compu. 12(9), 1273–1284 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  39. Yepez J.: Quantum lattice-gas model for the burgers equation. J. Stat. Phys. 107(1/2), 203–224 (2002)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for High Frequency Engineering, Technische Universität München, Arcisstrasse 21, 80333, Munich, Germany

    Siddhartha Sinha & Peter Russer

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  1. Siddhartha Sinha
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  2. Peter Russer
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Correspondence to Peter Russer.

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Sinha, S., Russer, P. Quantum computing algorithm for electromagnetic field simulation. Quantum Inf Process 9, 385–404 (2010). https://doi.org/10.1007/s11128-009-0133-x

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