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Adiabatic speedup in cutting a spin chain by pulse control in a laboratory frame

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Abstract

Techniques for the speedup of the adiabatic evolution by adding a leakage elimination operation (LEO) Hamiltonian to the system in an adiabatic frame have been developed recently. The LEO Hamiltonian can be implemented by a sequence of pulses, and the required pulse conditions for obtaining the effective adiabatic speedup have been analyzed. However, the required pulses obtained in an adiabatic frame have to be transformed into the forms in a laboratory frame since the pulses need to be added in a laboratory frame in an experiment. In this paper, we add an LEO Hamiltonian directly in a laboratory frame and find that the required pulse conditions obtained in the adiabatic frame are no longer valid. By exact numerical calculation, we obtain the new pulse conditions in the laboratory frame. We discuss the adiabatic speedup for different types of pulses using the process of cutting a ring spin chain as an example. The fidelity which measures the adiabaticity is found to be nearly one by carefully designing the pulse period and strength for a predefined time. Our scheme is more feasible to be realized in a practical experiment, since the physical implementation of the pulses is a challenging task after a transformation from an adiabatic frame to a laboratory frame.

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References

  1. Born, M., Fock, V.: Beweis des adiabatensatzes. Zeitschrift für Physik 51(3–4), 165 (1928)

    ADS  MATH  Google Scholar 

  2. Barends, R., Shabani, A., Lamata, L., Kelly, J., Mezzacapo, A., Las Heras, U., Babbush, R., Fowler, A.G., Campbell, B., Chen, Y., et al.: Digitized adiabatic quantum computing with a superconducting circuit. Nature 534(7606), 222 (2016)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  4. Mandrà, S., Guerreschi, G.G., Aspuru-Guzik, A.: Adiabatic quantum optimization in the presence of discrete noise: reducing the problem dimensionality. Phys. Rev. A 92, 062320 (2015)

    ADS  Google Scholar 

  5. Pyshkin, P.V., Luo, D., Jing, J., You, J.Q., Wu, L.A.: Expedited holonomic quantum computation in decoherence-free subspace. Sci. Rep. 6, 37781 (2016)

    ADS  Google Scholar 

  6. Barends, R., Shabani, A., Lamata, L., et al.: Digitized adiabatic quantum computing with a superconducting circuit. Nature 534, 222–226 (2016)

    ADS  Google Scholar 

  7. Tameem Albash, D.A.L.: arXiv:1611.04471 (2018)

  8. Balachandran, V., Gong, J.: Adiabatic quantum transport in a spin chain with a moving potential. Phys. Rev. A 77(1), 012303 (2008)

    ADS  Google Scholar 

  9. Farooq, U., Bayat, A., Mancini, S., Bose, S.: Adiabatic many-body state preparation and information transfer in quantum dot arrays. Phys. Rev. B 91, 134303 (2015)

    ADS  Google Scholar 

  10. Steffen, M., van Dam, W., Hogg, T., Breyta, G., Chuang, I.: Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90, 067903 (2003)

    ADS  Google Scholar 

  11. 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)

    ADS  Google Scholar 

  12. 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 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  13. Garnerone, S., Zanardi, P., Lidar, D.A.: Adiabatic quantum algorithm for search engine ranking. Phys. Rev. Lett. 108, 230506 (2012)

    ADS  Google Scholar 

  14. Boixo, S., Rønnow, T.F., Isakov, S.V., Wang, Z., Wecker, D., Lidar, D.A., Martinis, J.M., JTroyer, M.: Evidence for quantum annealing with more than one hundred qubits. Nat. Phys. 10(3), 218 (2014)

    Google Scholar 

  15. Wang, Z.M., Luo, D.W., Byrd, M.S., Wu, L.A., Yu, T., Shao, B.: Adiabatic speedup in a non-Markovian quantum open system. Phys. Rev. A 98, 062118 (2018)

    ADS  Google Scholar 

  16. Vacchini, B.: Book Review: the theory of open quantum systems. By H.-P. Breuer and F. Petruccione. Found. Phys. 34(1), 183 (2004)

    ADS  Google Scholar 

  17. Gardiner, C.W., Zoller, P.: Quantum noise a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Springer, Berlin (2004)

    MATH  Google Scholar 

  18. Wu, L.A.: http://www.authorstream.com/Presentation/james405702-2822542-universalleo/. Accessed 2016

  19. Lewis Jr., H.R., Riesenfeld, W.: An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10(8), 1458 (1969)

    ADS  MATH  Google Scholar 

  20. Gao, X.C., Xu, J.B., Qian, T.Z.: Geometric phase and the generalized invariant formulation. Phys. Rev. A 44(11), 7016 (1991)

    ADS  MathSciNet  Google Scholar 

  21. Lohe, M.: Exact time dependence of solutions to the time-dependent Schrödinger equation. J. Phys. A Math. Theor. 42(3), 035307 (2008)

    ADS  MATH  Google Scholar 

  22. Berry, M.V.: Transitionless quantum driving. J. Phys. A Math. Theor. 42(36), 365303 (2009)

    MathSciNet  MATH  Google Scholar 

  23. Demirplak, M., Rice, S.A.: Adiabatic population transfer with control fields. J. Phys. Chem. A 107(46), 9937 (2003)

    Google Scholar 

  24. Demirplak, M., Rice, S.A.: Adiabatic population transfer with control fields. J. Chem. Phys. 129(15), 154111 (2008)

    ADS  Google Scholar 

  25. Bason, M.G., Viteau, M., Malossi, N., Huillery, P., Arimondo, E., Ciampini, D., Fazio, R., Giovannetti, V., Mannella, R., Morsch, O.: High-fidelity quantum driving. Nat. Phys. 8(2), 147 (2012)

    Google Scholar 

  26. Dou, F.Q., Liu, J., Fu, B.: High-fidelity superadiabatic population transfer of a two-level system with a linearly chirped Gaussian pulse. EPL (Europhys. Lett.) 116(6), 60014 (2017)

    ADS  Google Scholar 

  27. Deng, S., Chenu, A., Diao, P., Li, F., Yu, S., Coulamy, I., Del Campo, A., Wu, H.: Superadiabatic quantum friction suppression in finite-time thermodynamics. Sci. Adv. 4(4), eaar5909 (2018)

    ADS  Google Scholar 

  28. Zhang, J., Shim, J.H., Niemeyer, I., Taniguchi, T., Teraji, T., Abe, H., Onoda, S., Yamamoto, T., Ohshima, T., Isoya, J., et al.: Experimental implementation of assisted quantum adiabatic passage in a single spin. Phys. Rev. Lett. 110(24), 240501 (2013)

    ADS  Google Scholar 

  29. Vasilev, G., Kuhn, A., Vitanov, N.: Optimum pulse shapes for stimulated Raman adiabatic passage. Phys. Rev. A 80(1), 013417 (2009)

    ADS  Google Scholar 

  30. Guérin, S., Hakobyan, V., Jauslin, H.: Optimal adiabatic passage by shaped pulses: efficiency and robustness. Phys. Rev. A 84(1), 013423 (2011)

    ADS  Google Scholar 

  31. Torrontegui, E., Ibánez, S., Martínez-Garaot, S., Modugno, M., del Campo, A., Guéry-Odelin, D., Ruschhaupt, A., Chen, X., Muga, J.G.: In Advances in atomic, molecular, and optical physics, vol. 62, pp. 117–169. Elsevier, Amsterdam (2013)

    Google Scholar 

  32. Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.: Shortcut to adiabatic passage in two-and three-level atoms. Phys. Rev. Lett. 105(12), 123003 (2010)

    ADS  Google Scholar 

  33. Pyshkin, P., Luo, D.W., Jing, J., You, J., Wu, L.A.: Expedited holonomic quantum computation via net zero-energy-cost control in decoherence-free subspace. Sci. Rep. 6, 37781 (2016)

    ADS  Google Scholar 

  34. Oh, S., Wu, L.A., Shim, Y.P., Fei, J., Friesen, M., Hu, X.: Heisenberg spin bus as a robust transmission line for quantum-state transfer. Phys. Rev. A 84(2), 022330 (2011)

    ADS  Google Scholar 

  35. Wang, Z.M., Bishop, C.A., Jing, J., Gu, Y.J., Garcia, C., Wu, L.A.: Shortcut to nonadiabatic quantum state transmission. Phys. Rev. A 93(6), 062338 (2016)

    ADS  Google Scholar 

  36. Malossi, N., Bason, M.G., Viteau, M., Arimondo, E., Mannella, R., Morsch, O., Ciampini, D.: Quantum driving protocols for a two-level system: from generalized Landau-Zener sweeps to transitionless control. Phys. Rev. A 87, 012116 (2013)

    ADS  Google Scholar 

  37. Giannelli, L., Arimondo, E.: Three-level superadiabatic quantum driving. Phys. Rev. A 89, 033419 (2014)

    ADS  Google Scholar 

  38. Theisen, M., Petiziol, F., Carretta, S., Santini, P., Wimberger, S.: Superadiabatic driving of a three-level quantum system. Phys. Rev. A 96, 013431 (2017)

    ADS  Google Scholar 

  39. Wang, Z.M., Byrd, M.S., Jing, J., Wu, L.A.: Adiabatic leakage elimination operator in an experimental framework. Phys. Rev. A 97(6), 062312 (2018)

    ADS  Google Scholar 

  40. Ren, F.H., Wang, Z.M., Gu, Y.J.: Shortcuts to adiabaticity in cutting a spin chain. Phys. Lett. A 381(2), 70 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  41. Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen, A., Sen, U.: Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56(2), 243 (2007)

    ADS  Google Scholar 

  42. Wu, L.A., Kurizki, G., Brumer, P.: Master equation and control of an open quantum system with leakage. Phys. Rev. Lett. 102, 080405 (2009)

    ADS  Google Scholar 

  43. Jing, J., Wu, L.A., Byrd, M., You, J.Q., Yu, T., Wang, Z.M.: Nonperturbative leakage elimination operators and control of a three-level system. Phys. Rev. Lett. 114, 190502 (2015)

    ADS  Google Scholar 

  44. Zhang, L.C., Ren, F.H., Chen, Y.F., He, R.H., Gu, Y.J., Wang, Z.M.: Adiabatic speedup via zero-energy-change control in a spin system. Epl 125, 1 (2019)

    Google Scholar 

  45. Viola, L., Knill, E., Lloyd, S.: Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  46. Vitali, D., Tombesi, P.: Using parity kicks for decoherence control. Phys. Rev. A 59, 4178 (1999)

    ADS  Google Scholar 

  47. Wang, Z.M., Wu, L.A., Jing, J., Shao, B., Yu, T.: Nonperturbative dynamical decoupling control: a spin-chain model. Phys. Rev. A 86, 032303 (2012)

    ADS  Google Scholar 

  48. Jing, J., Sarandy, M.S., Lidar, D.A., Luo, D.W., Wu, L.A.: Eigenstate tracking in open quantum systems. Phys. Rev. A 94, 042131 (2016)

    ADS  Google Scholar 

  49. Zhao-Ming Wang, L.A.W., Sarandy, Marcelo S.: arXiv:2005.01311 (2020)

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Acknowledgements

This material is based upon work supported by the NSFC (Grants No. 11475160, No. 61575180) and the Natural Science Foundation of Shandong Province (Grants No. ZR2014AM023, No. ZR2014AQ026). Z.M.W. thanks the China Scholarship Council (CSC) No. 201606335034 for this scholarship.

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Authors and Affiliations

  1. Department of Physics, Ocean University of China, Qingdao, 266100, China

    Rui Wang, Yong-Jian Gu & Zhao-Ming Wang

  2. College of Information and Control Engineering, Qingdao Technology University, Qingdao, 266520, China

    Feng-Hua Ren

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  1. Rui Wang
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Wang, R., Ren, FH., Gu, YJ. et al. Adiabatic speedup in cutting a spin chain by pulse control in a laboratory frame. Quantum Inf Process 19, 280 (2020). https://doi.org/10.1007/s11128-020-02779-2

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