Skip to main content
SpringerLink
Log in

Optimal controls of invariant-based population transfer in a superconducting qutrit

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Optimization of the control operations is of critical importance in the context of quantum information processing. We adopt optimal control techniques to implement invariant-based quantum population transfer in a superconducting qutrit. The first three levels of a charge-phase quantum circuit constitute an effective qutrit. By applying two microwave drivings, a \(\Lambda \)-configuration interaction appears in the qutrit. The population transfers can be performed using the invariant-based shortcuts. Particularly, taking the methods of optimal control in resonant and non-resonant cases, we implement the accelerated transfer operation in which the noise effects can be reduced greatly, and realize the high transfer insensitivity to deviation error of Rabi coupling, respectively. Our strategy could offer a promising approach to investigate robust state transfer with superconducting artificial atoms experimentally.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bergmann, K., Theuer, H., Shore, B.W.: Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003 (1998)

    ADS  Google Scholar 

  2. Mei, F., Feng, M., Yu, Y.-F., Zhang, Z.-M.: Scalable quantum information processing with atomic ensembles and flying photons. Phys. Rev. A 80, 042319 (2009)

    ADS  Google Scholar 

  3. Kurz, C., Schug, M., Eich, P., Huwer, J., Müller, P., Eschner, J.: Experimental protocol for high-fidelity heralded photon-to-atom quantum state transfer. Nat. Commun. 5, 5527 (2014)

    ADS  Google Scholar 

  4. Di Stefano, P.G., Paladino, E., D’Arrigo, A., Falci, G.: Population transfer in a Lambda system induced by detunings. Phys. Rev. B 91, 224506 (2015)

    ADS  Google Scholar 

  5. Beaudoin, F., Blais, A., Coish, W.A.: Hamiltonian engineering for robust quantum state transfer and qubit readout in cavity QED. New J. Phys. 19, 023041 (2017)

    ADS  Google Scholar 

  6. Kurpiers, P., et al.: Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264 (2018)

    ADS  Google Scholar 

  7. Feng, Z.-B., Cai, Z.-L., Zhang, C., Fan, L., Feng, T.: Quantum information transfer with Cooper-pair box qubits in circuit QED. Opt. Commun. 283, 1975 (2010)

    ADS  Google Scholar 

  8. Chen, X., Muga, J.G.: Engineering of fast population transfer in three-level systems. Phys. Rev. A 86, 033405 (2012)

    ADS  Google Scholar 

  9. Feng, Z.-B.: Robust quantum state transfer between a Cooper-pair box and diamond nitrogen-vacancy centers. Phys. Rev. A 91, 032307 (2015)

    ADS  Google Scholar 

  10. Wendin, G.: Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017)

    ADS  MathSciNet  Google Scholar 

  11. Gu, X., Kockum, A.F., Miranowicz, A., Liu, Y.-X., Nori, F.: Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  12. Liu, W.-Y., Zheng, D.-N., Zhao, S.-P.: Superconducting quantum bits. Chin. Phys. B 27, 027401 (2018)

    ADS  Google Scholar 

  13. Falci, G., Cognata, A.L., Berritta, M., D’Arrigo, A., Paladino, E., Spagnolo, B.: Design of a Lambda system for population transfer in superconducting nanocircuits. Phys. Rev. B 87, 214515 (2013)

    ADS  Google Scholar 

  14. Feng, Z.-B.: Quantum state transfer between hybrid qubits in a circuit QED. Phys. Rev. A 85, 014302 (2012)

    ADS  Google Scholar 

  15. Xu, P., Yang, X.-C., Mei, F., Xue, Z.-Y.: Controllable high-fidelity quantum state transfer and entanglement generation in circuit QED. Sci. Rep. 6, 18695 (2016)

    ADS  Google Scholar 

  16. Li, X., et al.: Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings. Phys. Rev. Appl. 10, 054009 (2018)

    ADS  Google Scholar 

  17. Feng, Z.-B., Yan, R.-Y., Zhou, Y.-Q.: Quantum state transfer with a two-dimensional Cooper-pair box qubit array. Quantum Inf. Process. 40, 1429 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  18. Liu, T., Xiong, S.-J., Cao, X.-Z., Su, Q.-P., Yang, C.-P.: Efficient transfer of an arbitrary qutrit state in circuit quantum electrodynamics. Opt. Lett. 40, 5602 (2015)

    ADS  Google Scholar 

  19. Kumar, K.S., Vepsäläinen, A., Danilin, S., Paraoanu, G.S.: Stimulated Raman adiabatic passage in a three-level superconducting circuit. Nat. Commun. 7, 10628 (2016)

    ADS  Google Scholar 

  20. Xu, H.K., et al.: Coherent population transfer between uncoupled or weakly coupled states in ladder-type superconducting qutrits. Nat. Commun. 7, 11018 (2016)

    ADS  Google Scholar 

  21. Chirolli, L., Burkard, G.: Decoherence in solid state qubits. Adv. Phys. 57, 225 (2008)

    ADS  Google Scholar 

  22. Paladino, E., Galperin, Y.M., Falci, G., Altshuler, B.L.: 1/f noise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361 (2014)

    ADS  Google Scholar 

  23. Solinas, P., Pirkkalainen, J.-M., Möttönen, M.: Ground-state geometric quantum computing in superconducting systems. Phys. Rev. A 82, 052304 (2010)

    ADS  Google Scholar 

  24. Dong, D., Chen, C., Qi, B., Petersen, I.R., Nori, F.: Robust manipulation of superconducting qubits in the presence of fluctuations. Sci. Rep. 5, 7873 (2015)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  26. Torrontegui, E., et al.: Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117 (2013)

    ADS  Google Scholar 

  27. Wu, J.-L., Ji, X., Zhang, S.: Fast adiabatic quantum state transfer and entanglement generation between two atoms via dressed states. Sci. Rep. 7, 46255 (2017)

    ADS  Google Scholar 

  28. Wu, J.L., Su, S.L.: Universal speeded-up adiabatic geometric quantum computation in three-level systems via counterdiabatic driving. J. Phys. A Math. Theor. 52, 335301 (2019)

    ADS  MathSciNet  Google Scholar 

  29. Vepsäläinen, A., Danilin, S., Paraoanu, G.S.: Optimal superadiabatic population transfer and gates by dynamical phase corrections. Quantum Sci. Technol. 3, 024006 (2018)

    ADS  Google Scholar 

  30. Wang, T., et al.: The experimental realization of high-fidelity ‘shortcut-to-adiabaticity’ quantum gates in a superconducting Xmon qubit. New J. Phys. 20, 065003 (2018)

    ADS  Google Scholar 

  31. Feng, Z.-B., Lu, X.-J., Yan, R.-Y., Zhao, Z.-Y.: Fast and robust population transfer with a Josephson qutrit via shortcut to adiabaticity. Sci. Rep. 8, 9310 (2018)

    ADS  Google Scholar 

  32. Ma, L.-H., Kang, Y.-H., Shi, Z.-C., Huang, B.-H., Song, J., Xia, Y.: Shortcuts to adiabatic for implementing controlled phase gate with Cooper-pair box qubits in circuit quantum electrodynamics system. Quantum Inf. Process. 18, 65 (2019)

    ADS  MATH  Google Scholar 

  33. Yan, T., et al.: Experimental realization of nonadiabatic shortcut to non-Abelian geometric gates. Phys. Rev. Lett. 122, 080501 (2019)

    ADS  Google Scholar 

  34. Vepsäläinen, A., Danilin, S., Paraoanu, G.S.: Superadiabatic population transfer in a three-level superconducting circuit. Sci. Adv. 5, eaau5999 (2019)

    ADS  Google Scholar 

  35. Peirce, A.P., Dahleh, M.A., Rabitz, H.: Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950 (1988)

    ADS  MathSciNet  Google Scholar 

  36. Roloff, R., Wenin, M., Pötz, W.: Optimal control for open quantum systems: qubits and quantum gates. J. Comput. Theor. Nanosci. 6, 1837 (2009)

    Google Scholar 

  37. Spörl, A., Schulte-Herbrüggen, T., Glaser, S.J., Bergholm, V., Storcz, M.J., Ferber, J., Wilhelm, F.K.: Optimal control of coupled Josephson qubits. Phys. Rev. A 75, 012302 (2007)

    ADS  Google Scholar 

  38. Lucero, E., et al.: Reduced phase error through optimized control of a superconducting qubit. Phys. Rev. A 82, 042339 (2010)

    ADS  Google Scholar 

  39. Chen, Z., et al.: Measuring and suppressing quantum state leakage in a superconducting qubit. Phys. Rev. Lett. 116, 020501 (2016)

    ADS  Google Scholar 

  40. Bao, S., Kleer, S., Wang, R., Rahmani, A.: Optimal control of superconducting gmon qubits using Pontryagin’s minimum principle: preparing a maximally entangled state with singular bang–bang protocols. Phys. Rev. A 97, 062343 (2018)

    ADS  Google Scholar 

  41. Vion, D., Aassime, A., Cottet, A., Joyez, P., Pothier, H., Urbina, C., Esteve, D., Devoret, M.H.: Manipulating the quantum state of an electrical circuit. Science 296, 886 (2002)

    ADS  Google Scholar 

  42. Feng, Z.-B., Lu, X.-J., Li, M., Yan, R.-Y., Zhou, Y.-Q.: Speeding up adiabatic population transfer in a Josephson qutrit via counter-diabatic driving. New J. Phys. 19, 123023 (2017)

    ADS  Google Scholar 

  43. Lu, X.-J., Li, M., Zhao, Z.Y., Zhang, C.-L., Han, H.-P., Feng, Z.-B., Zhou, Y.-Q.: Nonleaky and accelerated population transfer in a transmon qutrit. Phys. Rev. A 96, 023843 (2017)

    ADS  Google Scholar 

  44. Feng, Z.-B., Li, M.: High-fidelity population transfer in a Josephson three-level atom with optimized level anharmonicity. Opt. Commun. 319, 56 (2014)

    ADS  Google Scholar 

  45. Hioe, F.T.: Gell-Mann dynamic symmetry for N-level quantum systems. Phys. Rev. A 32, 2824 (1985)

    ADS  Google Scholar 

  46. Lewis, H.R., Riesenfeld, W.B.: 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, 1458 (1969)

    ADS  MathSciNet  MATH  Google Scholar 

  47. Lewis, H.R., Leach, P.G.: A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians. J. Math. Phys. 23, 2371 (1982)

    ADS  MathSciNet  MATH  Google Scholar 

  48. Dhara, A.K., Lawande, S.W.: Feynman propagator for time-dependent Lagrangians possessing an invariant quadratic in momentum. J. Phys. A Math. Gen. 17, 2324 (1984)

    MathSciNet  MATH  Google Scholar 

  49. Bruns, A., Genov, G.T., Hain, M., Vitanov, N.V., Halfmann, T.: Experimental demonstration of composite stimulated Raman adiabatic passage. Phys. Rev. A 98, 053413 (2018)

    ADS  Google Scholar 

  50. Yan, R.-Y., Yang, F., Zhang, N., Feng, Z.-B.: Accelerated and robust population transfer in a transmon qutrit via Delta-type driving. Quantum Inf. Process. 17, 237 (2018)

    ADS  MATH  Google Scholar 

  51. Yan, R.-Y., Feng, Z.-B., Zhang, C.-L., Li, M., Lu, X.-J., Zhou, Y.-Q.: Fast generations of entangled states between a transmon qubit and microwave photons via shortcuts to adiabaticity. Laser Phys. Lett. 15, 115205 (2018)

    ADS  Google Scholar 

  52. Blais, A., Gambetta, J., Wallraff, A., Schuster, D.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)

    ADS  Google Scholar 

  53. Lu, X.-J., Chen, X., Ruschhaupt, A., Alonso, D., Guérin, S., Muga, J.G.: Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors. Phys. Rev. A 88, 033406 (2013)

    ADS  Google Scholar 

  54. Daems, D., Ruschhaupt, A., Sugny, D., Guérin, S.: Robust quantum control by a single-shot shaped pulse. Phys. Rev. Lett. 111, 050404 (2013)

    ADS  Google Scholar 

Download references

Acknowledgements

The authors thank Professor X. Chen for valuable discussions. This work is supported by the Key Research Project in Universities of Henan Province (Grant Nos. 19A140016, 20B140016) and the “316” Project Plan of Xuchang University.

Author information

Authors and Affiliations

  1. School of Electric and Mechatronics Engineering, Xuchang University, Xuchang, 461000, China

    Zhi-Bo Feng & Xiao-Jing Lu

Authors
  1. Zhi-Bo Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Jing Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Jing Lu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feng, ZB., Lu, XJ. Optimal controls of invariant-based population transfer in a superconducting qutrit. Quantum Inf Process 19, 83 (2020). https://doi.org/10.1007/s11128-020-2583-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-2583-0

Keywords

Search

Navigation