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Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?

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Abstract

It has been known that when an assisted driving item is added to the main system Hamiltonian, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that only through adding an assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail. Thus the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately, the adiabatic computation may still fail. More importantly, we find that the adiabatic computation can only succeed if the assisted driving Hamiltonian has a relatively fixed form. This may help us understand why in the related literature all of the driving Hamiltonians used share the same form.

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References

  1. Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472–475 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Aharonov, D., Dam, Wv, Kempe, J., Landau, Z., Lloyd, S., Regev, O.: Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J. Comput. 37(1), 166–194 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mizel, A., Lidar, D.A., Mitchell, M.: Simple proof of equivalence between adiabatic quantum computation and the circuit model. Phys. Rev. Lett. 99(7), 070502 (2007)

    Article  ADS  Google Scholar 

  4. Messiah, A.: Quantum Mechanics. Dover, New York (1999)

    MATH  Google Scholar 

  5. Avron, J.E., Elgart, A.: Adiabatic theorem without a gap condition. Commun. Math. Phys. 203(2), 445–463 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Grover, L.K.: Quantum mechanics helps in searching for a needle in a Haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)

    Article  ADS  Google Scholar 

  7. Farhi, E., Goldstone, J., Gutmann, S.: Quantum adiabatic evolution algorithms with different paths. arXiv preprint arXiv:quant-ph/0208135 (2002)

  8. Sun, J., Lu, S., Braunstein, S.L.: On models of nonlinear evolution paths in adiabatic quantum algorithms. Commun. Theor. Phys. 59(1), 22–26 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Sun, J., Lu, S.: On the adiabatic evolution of one-dimensional projector Hamiltonians. Int. J. Quantum Inf. 10(4), 1250046 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sun, J., Lu, S.F., Liu, F.: Speedup in adiabatic evolution based quantum algorithms. Sci China Phys. Mech. Astron. 55(9), 1630–1634 (2012)

    Article  ADS  Google Scholar 

  11. Roland, J., Cerf, N.J.: Quantum search by local adiabatic evolution. Phys. Rev. A 65(4), 042308 (2002)

    Article  ADS  Google Scholar 

  12. Andrecut, M., Ali, M.K.: Unstructured adiabatic quantum search. Int. J. Theor. Phys. 43(4), 925–931 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  14. Altshuler, B., Krovi, H., Roland, J.: Anderson localization makes adiabatic quantum optimization fail. Proc. Natl. Acad. Sci. USA 107(28), 12446–12450 (2010)

    Article  ADS  MATH  Google Scholar 

  15. Åberg, J., Kult, D., Sjöqvist, E.: Robustness of the adiabatic quantum search. Phys. Rev. A 71(6), 060312 (2005)

    Article  Google Scholar 

  16. Sarandy, M.S., Lidar, D.A.: Adiabatic quantum computation in open systems. Phys. Rev. Lett. 95(25), 250503 (2005)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 61402188 and the Natural Science Foundation of Hubei Province under Grant No. 2016CFB541. This work was also supported by the Applied Basic Research Program of Wuhan Science and Technology Bureau under Grant No. 2016010101010003. The authors should also thank the anonymous referees for very useful comments which help improve the quality of this paper in its present form for clarity and readability.

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Authors and Affiliations

  1. School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jie Sun & Songfeng Lu

  2. College of Educational Information and Technology, Hubei Normal University, Huangshi, 435002, China

    Jie Sun

  3. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Li Li

Authors
  1. Jie Sun
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  2. Songfeng Lu
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  3. Li Li
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Correspondence to Songfeng Lu.

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Sun, J., Lu, S. & Li, L. Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?. Quantum Inf Process 16, 102 (2017). https://doi.org/10.1007/s11128-017-1553-7

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  • DOI: https://doi.org/10.1007/s11128-017-1553-7

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