Resonant transition-based quantum computation

  • Chen-Fu Chiang
  • Chang-Yu Hsieh


In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians’ spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.


Quantum Computation Resonant Transition Quantum Algorithm Bloch Sphere Quantum Device 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



C. C. gratefully acknowledges the support from the State University of New York Polytechnic Institute.


  1. 1.
    Deutsch, D., Jozsa, R.: Rapid solutions of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th IEEE Symposium on Foundations of Computer Science. pp. 124–134 (1994)Google Scholar
  3. 3.
    Denchev, V., Boixo, S., Isakov, S., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., Neven, H.: What is the computational value of finite range tunneling. arXiv:1512.02206 [quant-ph]
  4. 4.
    Crosson, E., Harrow, A.: Simulated quantum annealing can be exponentially faster than classical simulated annealing. arXiv:1601.03030 [quant-ph]
  5. 5.
    Farhi, E., Goldston, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. MIT-CTP-2936 (2000)Google Scholar
  6. 6.
    Dam, V., Mosca, M., Vazirani, U.: How powerful is adiabatic quantum computation, FOCS ’01. In: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, pp. 279–287 (2001)Google Scholar
  7. 7.
    Wang, H., Ashhab, S., Nori, F.: Quantum algorithm for obtaining the energy spectrum of a physical system. Phys. Rev. A 85, 062304 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Wang, H., Fan, H., Li, F.: A quantum algorithm for solving some discrete mathematical problems by probing their energy spectra. Phys. Rev. A 89, 012306 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    Wiebe, N., Berry, D., Hyer, P., Sander, B.: Simulating quantum dynamics on a quantum computer. J. Phys. A: Math. Theor. 44(44) (2011)Google Scholar
  10. 10.
    Laumann, C., Moessner, R., Scardicchio, A., Sondhi, S.: Quantum annealing: the fastest route to quantum computation? Eur. Phys. J. Spec. Top. 224, 75 (2015)CrossRefGoogle Scholar
  11. 11.
    Wang, H., Ashhab, S., Nori, F.: Quantum algorithm for simulating the dynamics of an open quantum system. Phys. Rev. A 83, 062317 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Scully, M., Zubairy, M.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefMATHGoogle Scholar
  13. 13.
    Terhal, B., DiVincenzo, D.: Problem of equilibration and the computation of correlation functions on a quantum computer. Phys. Rev. A 61, 022301 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    Wang, H.: Quantum algorithm for obtaining the eigenstates of a physical system. Phys. Rev. A 93, 052334 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    Biamonte, J., Love, P.: Realizable hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008)ADSMathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Biamonte, J.: Non-perturbative k-body to two-body commuting conversion hamiltonians and embedding problem instances into Ising spins. Phys. Rev. A 77, 052331 (2008)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Liu, W.Z., Zhang, J.F., Deng, Z.W., Long, G.L.: Simulation of general three-body interactions in a nulcear magnetic resonance ensemble quantum computer. Sci. China Ser. G Phys. Mech. Astron. 51, 1089–1096 (2008)ADSCrossRefMATHGoogle Scholar
  18. 18.
    Cetina, M., Bylinskii, A., Karpa, L., Gangloff, D., Beck, K.M., Ge, Y., Scholz, M., Grier, A.T., Chuang, I., Vuletic, V.: One-dimensional array of ion chains coupled to an optical cavity. New J. Phys. 15, 053001 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    Messiah, A.: Quantum Mechanics, vol. II. Amsterdam, Wiley, North Holland, New York (1976)MATHGoogle Scholar
  20. 20.
    Wong, T., Meyer, D.: Irreconcilable difference between quantum walks and adiabatic quantum computing. Phys. Rev. A 93, 062313 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Mézard, M., Parisi, G., Zecchian, R.: Analytic and algorithmic solution of random satisfiability problems. Science 297(5582), 812–815 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    Peng, X., Liao, Z., Xu, N., Qin, G., Zhou, X., Suter, D., Du, J.: Quantum adiabatic algorithm for factorization and its experimental implementation. Phys. Rev. Lett. 101, 220405 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    Crawford, J., Auton, L.: Experimental results on the crossover point in satisfiability problems. In: Proceedings of the 11th National Conference on AI, pp. 21-27 (1993)Google Scholar
  24. 24.
    Mitchell, D., Selman, B., Levesque, H.: Hard and easy distributionsof SAT problems. In: Proceedings of the 10th National Conference on AI, pp. 459-465 (1992)Google Scholar
  25. 25.
    Huberman, B.A., Hogg, T.: Phase transitions in artificial intelligence systems. Artif. Intell. 33(2), 155–171 (1987)CrossRefGoogle Scholar
  26. 26.
    Garraway, B.: The Dicke model in quanutm optics: Dicke model revisited. Philos. Trans. R. Soc. A 369, 1137–1155 (2011)ADSMathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)Google Scholar
  28. 28.
    Ghoreishi, S., Sarbishaei, M., Jvidan, K.: Entanglement between two Tavis–Cummings systems with N = 2. Int. J. Theor. Math. Phys. 2(6), 187–195 (2012)CrossRefGoogle Scholar
  29. 29.
    Horvath, L., Sanders, B.: Photon coincidence spectroscopy for two-atom cavity quantum electrodynamics. J. Mod. Opt. 49(1–2), 285–303 (2002)ADSCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceState University of New York Polytechnic InstituteUticaUSA
  2. 2.Department of ChemistryMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations