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Fast and robust implementation of quantum gates by transitionless quantum driving

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Abstract

As a basic operation in quantum computers, quantum logic gates and particularly controlled NOT (CNOT) gates are important in quantum information processing. In this paper, we propose a one-step scheme to generate a CNOT gate via transitionless quantum driving. In this scheme, an effective Hamiltonian is obtained based on quantum Zeno dynamics to drive the system to evolve into the target state when the parameters are reasonably set. The results of explicit numerical simulations indicate that the proposed scheme is robust against instability related to variation in experimental parameters and decoherence. The scheme can also be extended to generate a Toffoli gate, which is useful for large-scale quantum computers. Moreover, the generation process involves only a single step, greatly simplifying its implementation.

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References

  1. Duan, L.M., Kinble, H.J.: Efficient engineering of multiatom entanglement through single-photon detections. Phys. Rev. Lett. 90, 253601 (2003)

    Article  ADS  Google Scholar 

  2. Neeley, M., Bialczak, R.C., Lenander, M., et al.: Generation of three-qubit entangled states using superconducting phase qubits. Nature 467, 570 (2010)

    Article  ADS  Google Scholar 

  3. Yang, C.P., Su, Q.P., Zheng, S.B., Han, S.: Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit. Phys. Rev. A 87, 022320 (2013)

    Article  ADS  Google Scholar 

  4. Huang, Y.F., Liu, B.H., Peng, L., et al.: Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state. Nat. Commun. 2, 546 (2011)

    Article  ADS  Google Scholar 

  5. Facchi, P., Gorini, V., Marmo, G., et al.: Quantum Zeno dynamics. Phys. Lett. A 275, 12 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Facchi, P., Pascazio, S.: Quantum Zeno and inverse quantum Zeno effects. Prog. Opt. 42, 147 (2001)

    Article  ADS  MATH  Google Scholar 

  7. Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Vitanov, N.V., Suominen, K.A., Shore, B.W.: Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage. J. Phys. B 32, 4535 (1999)

    Article  ADS  Google Scholar 

  10. Guery, D., et al.: Shortcuts to adiabaticity: concepts, methods, and applications. Rev. Mod. Phys. 91, 045001 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  11. 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Chen, X., Torrontegui, E., Muga, J.G.: Lewis–Riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Lu, M., Xia, Y., Shen, L.T., Song, J., An, N.B.: Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity. Phys. Rev. A 89, 012326 (2014)

    Article  ADS  Google Scholar 

  15. Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems. Phys. Rev. A 89, 033856 (2014)

    Article  ADS  Google Scholar 

  16. Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system. Phys. Rev. A 97, 023841 (2018)

    Article  ADS  Google Scholar 

  17. Berry, M.V.: Transitionless quantum driving. J. Phys. A 42, 365303 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. del Campo, A.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)

    Article  Google Scholar 

  19. Liang, Y., Wu, Q.C., Su, S.L., Ji, X., Zhang, S.: Shortcuts to adiabatic passage for multiqubit controlled-phase gate. Phys. Rev. A 91, 032304 (2015)

    Article  ADS  Google Scholar 

  20. Du, Y.X., Liang, Z.T., Li, Y.C., Yue, X.X., Lü, Q.X., Huang, W., Chen, X., Yan, H., Zhu, S.L.: Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms. Nat. Commun. 7, 12999 (2016)

    Article  Google Scholar 

  21. Zhou, B.B., Baksic, A., Ribeiro, H., et al.: Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system. Nat. Phys. 13, 330 (2017)

    Article  Google Scholar 

  22. Li, Y.C., Chen, X.: Shortcut to adiabatic population transfer in quantum three-level systems: effective two-level problems and feasible counterdiabatic driving. Phys. Rev. A 94, 063411 (2016)

    Article  ADS  Google Scholar 

  23. Zhou, X., Liu, B.J., Shao, L.B., Zhang, X.D., Xue, Z.Y.: Quantum state conversion in opto-electro-mechanical systems via shortcut to adiabaticity. Laser Phys. Lett. 14, 095202 (2017)

    Article  ADS  Google Scholar 

  24. Chen, Y.H., Xia, Y., Song, J., Chen, Q.Q.: Shortcuts to adiabatic passage for fast generation of Greenberger–Horne–Zeilinger states by transitionless quantum driving. Sci. Rep. 5, 15616 (2015)

    Article  ADS  Google Scholar 

  25. Masuda, S., Nakamura, K.: Acceleration of adiabatic quantum dynamics in electromagnetic fields. Phys. Rev. A 84, 043434 (2011)

    Article  ADS  Google Scholar 

  26. Masuda, S., Rice, S.A.: Fast-forward assisted STIRAP. J. Phys. Chem. A 119, 3479 (2015)

    Article  Google Scholar 

  27. Ibáñez, S., Chen, X., Torrontegui, E., et al.: Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity. Phys. Rev. Lett. 109, 100403 (2012)

    Article  ADS  Google Scholar 

  28. Ibáñez, S., Chen, X., Muga, J.G.: Improving shortcuts to adiabaticity by iterative interaction pictures. Phys. Rev. A 87, 043402 (2013)

    Article  ADS  Google Scholar 

  29. Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics. Phys. Rev. A 93, 052324 (2016)

    Article  ADS  Google Scholar 

  30. Baksic, A., Ribeiro, H., Clerk, A.A.: Speeding up adiabatic quantum state transfer by using dressed states. Phys. Rev. Lett. 116, 230503 (2016)

    Article  ADS  Google Scholar 

  31. Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Fast preparation of W states with superconducting quantum interference devices by using dressed states. Phys. Rev. A 94, 052311 (2016)

    Article  ADS  Google Scholar 

  32. Baksic, A., Belyansky, R., Ribeiro, H., Clerk, A.A.: Shortcuts to adiabaticity in the presence of a continuum: applications to itinerant quantum state transfer. Phys. Rev. A 96, 021801 (2017)

    Article  ADS  Google Scholar 

  33. Zhang, F.Y., Yang, C.P.: Tunable coupling of spin ensembles. Opt. Lett. 43, 466 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Chen, X., Ruschhaupt, A., Schmidt, S., et al.: Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. Phys. Rev. Lett. 104, 063002 (2010)

    Article  ADS  Google Scholar 

  36. Chen, Y.H., Wu, Q.C., Huang, B.H., Song, J., Xia, Y.: Arbitrary quantum state engineering in three-state systems via counterdiabatic driving. Sci. Rep. 6, 38484 (2016)

    Article  ADS  Google Scholar 

  37. Chen, Y.H., Shi, Z.C., Song, J., Xia, Y., Zheng, S.B.: Optimal shortcut approach based on an easily obtained intermediate Hamiltonian. Phys. Rev. A 95, 062319 (2017)

    Article  ADS  Google Scholar 

  38. Kang, Y.H., Chen, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm. Phys. Rev. A 96, 022304 (2017)

    Article  ADS  Google Scholar 

  39. Zheng, R.H., Kang, Y.H., Shi, Z.C., Xia, Y.: Complete and nondestructive atomic Bell-State analysis assisted by inverse engineering. Ann. Phys. (Berlin) 530, 1800133 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  40. Shan, W.J., Zhang, X.P., Wang, W.Q., Lin, M.: Fast and robust generation of singlet state via shortcuts to adiabatic passage. Quantum Inf. Process. 18, 22 (2018)

    Article  ADS  MATH  Google Scholar 

  41. Yu, W.R., Ji, X.: Fast preparing W state via a chosen path shortcut in circuit QED. Quantum Inf. Process. 18, 247 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  42. Gao, W.B., Xu, P., Yao, X.C., et al.: Experimental realization of a controlled-NOT Gate with Four-Photon Six-Qubit Cluster States. Phys. Rev. Lett. 104, 020501 (2010)

    Article  ADS  Google Scholar 

  43. Zeng, Y., Xu, P., He, X.D., et al.: Entangling two individual atoms of different isotopes via Rydberg blockade. Phys. Rev. Lett. 119, 160502 (2017)

    Article  ADS  Google Scholar 

  44. Tang, S.Q., Zhang, D.Y., Xie, L.J., Zhan, X.G., Gao, F.: Selective atom-cavity interaction scheme for quantum controlled-NOT gate using four-level atoms in cavity QED system. Commun. Theor. Phys. 51, 247 (2009)

    Article  ADS  Google Scholar 

  45. Cesa, A., Martin, J.: Two-qubit entangling gates between distant atomic qubits in a lattice. Phys. Rev. A 95, 052330 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  46. Rosenblum, S., Gao, Y.Y., Reinhold, P., et al.: A CNOT gate between multiphoton qubits encoded in two cavities. Nat. Commun. 9, 652 (2018)

    Article  ADS  Google Scholar 

  47. Noh, T., Park, G., Lee, S.G., Song, W., Chong, Y.: Construction of controlled-NOT gate based on microwave-activated phase (MAP) gate in two transmon system. Sci. Rep. 8, 13598 (2018)

    Article  ADS  Google Scholar 

  48. Sangouard, N., Lacour, X., Guérin, S., Jauslin, H.R.: CNOT gate by adiabatic passage with an optical cavity. Eur. Phys. J. D 37, 451 (2006)

    Article  ADS  Google Scholar 

  49. Liang, Y., Song, C., Ji, X., Zhang, S.: Fast CNOT gate between two spatially separated atoms via shortcuts to adiabatic passage. Opt. Express 23, 023798 (2015)

    Article  Google Scholar 

  50. Wu, J.L., Ji, X., Zhang, S.: Dressed-state scheme for a fast CNOT gate. Quantum Inf. Process. 16, 294 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Liu, S., Ran, D., Shi, Z.C., Song, J., Xia, Y.: Implementation of controlled-NOT gate by Lyapunov control. Ann. Phys. (Berlin) 531, 1900086 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  52. Zoubi, H., Orenstien, M., Ron, A.: Coupled microcavities with dissipation. Phys. Rev. A 62, 033801 (2000)

    Article  ADS  Google Scholar 

  53. Ogden, C.D., Irish, E.K., Kim, M.S.: Dynamics in a coupled-cavity array. Phys. Rev. A 78, 063805 (2008)

    Article  ADS  Google Scholar 

  54. Li, Q., Wang, T., Su, Y., Yan, M., Qiu, M.: Coupled mode theory analysis of mode-splitting in coupled cavity system. Opt. Express 18, 8367 (2010)

    Article  ADS  Google Scholar 

  55. Knap, M., Arrigoni, E., Linden, W.V.D.: Emission characteristics of laser-driven dissipative coupled-cavity systems. Phys. Rev. A 83, 023821 (2011)

    Article  ADS  Google Scholar 

  56. Wang, Z., Xia, Y., Chen, Y.H., Song, J.: Fast controlled preparation of two-atom maximally entangled state and N-atom W state in the direct coupled cavity systems via shortcuts to adiabatic passage. Eur. Phys. J. D 70, 162 (2016)

    Article  ADS  Google Scholar 

  57. Almeida, G.M.A., Ciccarello, F., Apollaro, T.J.G., Souza, A.M.C.: Quantum-state transfer in staggered coupled-cavity arrays. Phys. Rev. A 93, 032310 (2016)

    Article  ADS  Google Scholar 

  58. Lu, M., Zhang, C.L., Zhang, B., Lin, W.S.: Shortcuts to adiabatic passage for the generation of maximally entangle states in a distributed atom-cavity system. Laser Phys. Lett. 16, 045206 (2019)

    Article  ADS  Google Scholar 

  59. Hartmann, M.J., Brandão, F.G.S.L., Plenio, M.B.: Quantum many-body phenomena in coupled cavity arrays. Laser Photon. Rev. 2, 527 (2008)

    Article  ADS  Google Scholar 

  60. Kim, K.H., Hwang, M.S., Kim, H.R., Choi, J.H., No, Y.S., Park, H.G.: Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains. Nat. Commun. 7, 13893 (2016)

    Article  ADS  Google Scholar 

  61. Schiró, M., Joshi, C., Bordyuh, M., Fazio, R., Keeling, J., Türeci, H.E.: Exotic attractors of the nonequilibrium Rabi–Hubbard model. Phys. Rev. Lett. 116, 143603 (2016)

    Article  ADS  Google Scholar 

  62. Fitzpatrick, M., Sundaresan, N.M., Li, A.C.Y., Koch, J., Houck, A.A.: Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Phys. Rev. X 7, 011016 (2017)

    Google Scholar 

  63. Chen, M.F., Chen, Y.F., Ma, S.S.: One-step implementation of a Toffoli gate of separated superconducting qubits via quantum Zeno dynamics. Quantum Inf. Process 15, 1469 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. Li, H.O., Cao, G., Yu, G.D., et al.: Controlled quantum operations of a semiconductor three-qubit system. Phys. Rev. Appl. 9, 024015 (2018)

    Article  ADS  Google Scholar 

  65. Beterov, I.I., Ashkarin, I.N., et al.: Fast three-qubit Toffoli quantum gate based on three-body Förster resonances in Rydberg atoms. Phys. Rev. A 98, 042704 (2017)

    Article  ADS  Google Scholar 

  66. Cao, Y., Wang, G.C., Liu, H.D., Sun, C.F.: Implementation of a Tofoli gate using an array of coupled cavities in a single step. Sci. Rep. 8, 5813 (2018)

    Article  ADS  Google Scholar 

  67. Li, M., Zhang, M.: Robust universal photonic quantum gates operable with imperfect processes involved in diamond nitrogen-vacancy centers inside low-Q single-sided cavities. Opt. Express 26, 33129 (2018)

    Article  ADS  Google Scholar 

  68. Boozer, A.D., Boca, A., Miller, R., Northup, T.E., Kimble, H.J.: Cooling to the ground state of a xial motion for one atom strongly coupled to an optical cavity. Phys. Rev. Lett. 97, 083602 (2006)

    Article  ADS  Google Scholar 

  69. Mundt, A.B., Kreuter, A., Becher, C., Leibfried, D., Eschner, J., Schmidt-Kaler, F., Blatt, R.: Cooling a single atomic quantum bit to a high finesse optical cavity. Phys. Rev. Lett. 89, 103001 (2002)

    Article  ADS  Google Scholar 

  70. Spillane, S.M., Kippenberg, T.J., Vahala, K.J., Goh, K.W., Wilcut, E., Kimble, H.J.: Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)

    Article  ADS  Google Scholar 

  71. Buck, J.R., Kimble, H.J.: Optimal sizes of dielectric microspheres for cavity QED with strong coupling. Phys. Rev. A 67, 033806 (2003)

    Article  ADS  Google Scholar 

  72. Hartmann, M.J., Brandão, F.G.S.L., Plenio, M.B.: Strongly correlated polaritons in a two-dimensional array of cavities. Nat. Phys. 2, 849 (2006)

    Article  Google Scholar 

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Acknowledgements

This work is supported by the Educational Committee of Fujian Province of China under Grants Nos. JAT190978 and JT180729.

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Authors and Affiliations

  1. College of Artificial Intelligence, Yango University, Fuzhou, 350015, China

    Wen-Wu Liu, Chun-Ling Zhang & Ling Zhang

  2. Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials, College of Physics and Energy, Fujian Normal University, Fuzhou, 350117, China

    Chun-Ling Zhang

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  1. Wen-Wu Liu
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Liu, WW., Zhang, CL. & Zhang, L. Fast and robust implementation of quantum gates by transitionless quantum driving. Quantum Inf Process 20, 118 (2021). https://doi.org/10.1007/s11128-021-03038-8

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