Advertisement

Frontiers of Physics

, 15:21603 | Cite as

Transferring entangled states of photonic cat-state qubits in circuit QED

  • Tong Liu
  • Zhen-Fei Zheng
  • Yu Zhang
  • Yu-Liang Fang
  • Chui-Ping YangEmail author
Research Article
  • 8 Downloads

Abstract

We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resource is minimized. The entanglement transfer is completed with a singlestep operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two-cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.

Keywords

transferring quantum entangled states photonic cat-state microwave cavities 

Notes

Acknowledgements

This work was partly supported by the Key-Area Research and Development Program of GuangDong Province (Grant No. 2018B030326001), the National Natural Science Foundation of China (NSFC) (Grant Nos. 11074062, 11374083, and 11774076), the NKRDP of China (Grant No. 2016YFA0301802), and the Jiangxi Natural Science Foundation (Grant No. 20192ACBL20051).

References

  1. 1.
    C. P. Yang, S. I. Chu, and S. Han, Possible realization of entanglement, logical gates, and quantum information transfer with superconducting-quantuminterference-device qubits in cavity QED, Phys. Rev. A 67(4), 042311 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    J. Q. You and F. Nori, Quantum information processing with superconducting qubits in a microwave field, Phys. Rev. B 68(6), 064509 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69(6), 062320 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58(11), 42 (2005)CrossRefGoogle Scholar
  5. 5.
    J. Clarke and F. K. Wilhelm, Superconducting quantum bits, Nature 453(7198), 1031 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85(2), 623 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718–719, 1 (2017)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    P. B. Li, Y. C. Liu, S. Y. Gao, Z. L. Xiang, P. Rabl, Y. F. Xiao, and F. L. Li, Hybrid quantum device based on NV centers in diamond nanomechanical resonators plus superconducting waveguide cavities, Phys. Rev. Appl. 4(4), 044003 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    C. P. Yang, S. I. Chu, and S. Han, Quantum information transfer and entanglement with SQUID qubits in cavity QED: A dark-state scheme with tolerance for nonuniform device parameter, Phys. Rev. Lett. 92(11), 117902 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431(7005), 162 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong coupling regime, Nat. Phys. 6(10), 772 (2010)CrossRefGoogle Scholar
  13. 13.
    Q. Q. Wu, J. Q. Liao, and L. M. Kuang, Quantum state transfer between charge and flux qubits in circuit-QED, Chin. Phys. Lett. 25(4), 1179 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Z. B. Feng, Quantum state transfer between hybrid qubits in a circuit QED, Phys. Rev. A 85(1), 014302 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    C. P. Yang, Q. P. Su, and F. Nori, Entanglement generation and quantum information transfer between spatially-separated qubits in different cavities, New J. Phys. 15(11), 115003 (2013)ADSCrossRefGoogle Scholar
  16. 16.
    C. P. Yang and S. Han, n-qubit-controlled phase gate with superconducting quantum interference devices coupled to a resonator, Phys. Rev. A 72(3), 032311 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    C. P. Yang, Y. X. Liu, and F. Nori, Phase gate of one qubit simultaneously controlling n qubits in a cavity, Phys. Rev. A 81(6), 062323 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    C. P. Yang, Q. P. Su, F. Y. Zhang, and S. B. Zheng, Single-step implementation of a multiple target-qubit controlled phase gate without need of classical pulses, Opt. Lett. 39(11), 3312 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    H. F. Wang, A. D. Zhu, and S. Zhang, One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities, Opt. Lett. 39(6), 1489 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Z. P. Hong, B. J. Liu, J. Q. Cai, X. D. Zhang, Y. Hu, Z. D. Wang, and Z. Y. Xue, Implementing universal nonadiabatic holonomic quantum gates with transmons, Phys. Rev. A 97(2), 022332 (2018)ADSCrossRefGoogle Scholar
  21. 21.
    B. Ye, Z. F. Zheng, and C. P. Yang, Multiplex-controlled phase gate with qubits distributed in a multicavity system, Phys. Rev. A 97(6), 062336 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    S. L. Zhu, Z. D. Wang, and P. Zanardi, Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity, Phys. Rev. Lett. 94(10), 100502 (2005)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    X. L. Zhang, K. L. Gao, and M. Feng, Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED, Phys. Rev. A 74(2), 024303 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Z. J. Deng, K. L. Gao, and M. Feng, Generation of N-qubit W states with rf SQUID qubits by adiabatic passage, Phys. Rev. A 74(6), 064303 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    F. Helmer, and F. Marquardt, Measurement-based synthesis of multiqubit entangled states in superconducting cavity QED, Phys. Rev. A 79(5), 052328 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    S. Aldana, Y. D. Wang, and C. Bruder, Greenberger-Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus, Phys. Rev. B 84(13), 134519 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, Entangling superconducting qubits in a multi-cavity system, New J. Phys. 18(1), 013025 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    X. T. Mo, and Z. Y. Xue, Single-step multipartite entangled states generation from coupled circuit cavities, Front. Phys. 14(3), 31602 (2019)CrossRefGoogle Scholar
  29. 29.
    Y. Xu, W. Cai, Y. Ma, X. Mu, L. Hu, T. Chen, H. Wang, Y. P. Song, Z. Y. Xue, Z. Q. Yin, and L. Sun, Single-loop realization of arbitrary non-adiabatic holonomic single-qubit quantum gates in a superconducting circuit, Phys. Rev. Lett. 121(11), 110501 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    T. Wang, Z. Zhang, L. Xiang, Z. Jia, P. Duan, W. Cai, Z. Gong, Z. Zong, M. Wu, J. Wu, L. Sun, Y. Yin, and G. Guo, The experimental realization of high-fidelity “shortcut-to-adiabaticity” quantum gates in a superconducting Xmon qubit, arXiv: 1804.08247 (2018)Google Scholar
  31. 31.
    P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, Using sideband transitions for two-qubit operations in superconducting circuits, Phys. Rev. B 79, 180511(R) (2009)ADSCrossRefGoogle Scholar
  32. 32.
    J. M. Chow, A. D. Córcoles, J. M. Gambetta, C. Rigetti, B. R. Johnson, J. A. Smolin, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, Simple All-microwave entangling gate for fixed-frequency superconducting qubits, Phys. Rev. Lett. 107(8), 080502 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Implementing the quantum von neumann architecture with superconducting circuits, Science 334(6052), 61 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    A. Fedorov, L. Steffen, M. Baur, M. P. daSilva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481(7380), 170 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    C. Song, K. Xu, W. Liu, C. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, 10-qubit entanglement and parallel logic operations with a superconducting circuit, Phys. Rev. Lett. 119(18), 180511 (2017)ADSCrossRefGoogle Scholar
  36. 36.
    M. Gong, M. C. Chen, Y. Zheng, S. Wang, C. Zha, H. Deng, Z. Yan, H. Rong, Y. Wu, S. Li, F. Chen, Y. Zhao, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, A. D. Castellano, H. Wang, C. Peng, C. Y. Lu, X. Zhu, and J. W. Pan, Genuine12-qubit entanglement on a superconducting quantum processor, Phys. Rev. Lett. 122(11), 110501 (2019)ADSCrossRefGoogle Scholar
  37. 37.
    C. Song, K. Xu, H. Li, Y. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D. Wang, H. Wang, and S. Zhu, Observation of multi-component atomic Schrodinger cat states of up to 20 qubits, Science 365(6453), 574 (2019)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Lang, C. Eichler, G. Puebla-Hellmann, A. Fedorov, and A. Wallraff, Deterministic quantum teleportation with feed-forward in a solid state system., Nature 500(7462), 319 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z. Y. Xue, Z. Q. Yin, and L. Sun, Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings, Phys. Rev. Appl. 10(5), 054009 (2018)ADSCrossRefGoogle Scholar
  40. 40.
    W. Ning, X. J. Huang, P. R. Han, H. Li, H. Deng, Z. B. Yang, Z. R. Zhong, Y. Xia, K. Xu, D. Zheng, and S. B. Zheng, Deterministic entanglement swapping in a superconducting circuit, arXiv: 1902.10959 (2019)Google Scholar
  41. 41.
    Z. Yan, Y. R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, C. Z. Peng, K. Xia, H. Deng, H. Rong, J. Q. You, F. Nori, H. Fan, X. Zhu, and J. W. Pan, Strongly correlated quantum walks with a 12-qubit superconducting processor, Science 364(6442), 753 (2019)ADSCrossRefGoogle Scholar
  42. 42.
    W. Chen, D. A. Bennett, V. Patel, and J. E. Lukens, Substrate and process dependent losses in superconducting thin film resonators, Supercond. Sci. Technol. 21(7), 075013 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    P. J. Leek, M. Baur, J. M. Fink, R. Bianchetti, L. Steffen, S. Filipp, and A. Wallraff, Cavity quantum electrodynamics with separate photon storage and qubit readout modes, Phys. Rev. Lett. 104(10), 100504 (2010)ADSCrossRefGoogle Scholar
  44. 44.
    M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, A quantum memory with near-millisecond coherence in circuit QED, Phys. Rev. B 94(1), 014506 (2016)ADSCrossRefGoogle Scholar
  45. 45.
    M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339(6124), 1169 (2013)ADSCrossRefGoogle Scholar
  46. 46.
    M. Mariantoni, M. J. Storcz, F. K. Wilhelm, W. D. Oliver, A. Emmert, A. Marx, R. Gross, H. Christ, and E. Solano, On-chip microwave Fock states and quantum homodyne measurements, arXiv: cond-mat/0509737 (2005)Google Scholar
  47. 47.
    Y. X. Liu, L. F. Wei, and F. Nori, Generation of non-classical photon states using a superconducting qubit in a microcavity, Europhys. Lett. 67(6), 941 (2004)ADSCrossRefGoogle Scholar
  48. 48.
    K. Moon and S. M. Girvin, Theory of microwave parametric down-conversion and squeezing using circuit QED, Phys. Rev. Lett. 95(14), 140504 (2005)ADSCrossRefGoogle Scholar
  49. 49.
    F. Marquardt and C. Bruder, Superposition of two mesoscopically distinct quantum states: Coupling a Cooper-pair box to a large superconducting island, Phys. Rev. B 63(5), 054514 (2001)ADSCrossRefGoogle Scholar
  50. 50.
    Y. X. Liu, L. F. Wei, and F. Nori, Preparation of macroscopic quantum superposition states of a cavity field via coupling to a superconducting charge qubit, Phys. Rev. A 71(6), 063820 (2005)ADSCrossRefGoogle Scholar
  51. 51.
    J. Q. Liao, J. F. Huang, and L. Tian, Generation of macroscopic Schrödinger-cat states in qubit-oscillator systems, Phys. Rev. A (Coll. Park) 93(3), 033853 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    X. Y. Lü, G. L. Zhu, L. L. Zheng, and Y. Wu, Entanglement and quantum superposition induced by a single photon, Phys. Rev. A (Coll. Park) 97(3), 033807 (2018)ADSCrossRefGoogle Scholar
  53. 53.
    F. W. Strauch, K. Jacobs, and R. W. Simmonds, Arbitrary control of entanglement between two superconducting resonators, Phys. Rev. Lett. 105(5), 050501 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    C. P. Yang, Q. P. Su, and S. Han, Generation of Greenberger-Horne-Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction, Phys. Rev. A 86(2), 022329 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    P. B. Li, S. Y. Gao, and F. L. Li, Engineering two-mode entangled states between two superconducting resonators by dissipation, Phys. Rev. A 86(1), 012318 (2012)ADSCrossRefGoogle Scholar
  56. 56.
    C. P. Yang, Q. P. Su, S. B. Zheng, and S. Han, Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit, Phys. Rev. A 87(2), 022320 (2013)ADSCrossRefGoogle Scholar
  57. 57.
    Q. P. Su, H. H. Zhu, L. Yu, Y. Zhang, S. J. Xiong, J. M. Liu, and C. P. Yang, Generating double NOON states of photons in circuit QED, Phys. Rev. A 95(2), 022339 (2017)ADSCrossRefGoogle Scholar
  58. 58.
    C. P. Yang, Q. P. Su, S. B. Zheng, F. Nori, and S. Han, Entangling two oscillators with arbitrary asymmetric initial states, Phys. Rev. A 95(5), 052341 (2017)ADSCrossRefGoogle Scholar
  59. 59.
    S. T. Merkel and F. K. Wilhelm, Generation and detection of NOON states in superconducting circuits, New J. Phys. 12(9), 093036 (2010)ADSCrossRefGoogle Scholar
  60. 60.
    Y. J. Zhao, C. Q. Wang, X. Zhu, and Y. X. Liu, Engineering entangled microwave photon states via multiphoton transitions between two cavities and a superconducting qubit, arXiv: 1506.06363 (2015)Google Scholar
  61. 61.
    S. J. Xiong, Z. Sun, J. M. Liu, T. Liu, and C. P. Yang, Efficient scheme for generation of photonic NOON states in circuit QED, Opt. Lett. 40(10), 2221 (2015)ADSCrossRefGoogle Scholar
  62. 62.
    M. Hua, M. J. Tao, and F. G. Deng, Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics, Phys. Rev. A 90(1), 012328 (2014)ADSCrossRefGoogle Scholar
  63. 63.
    M. Hua, M. J. Tao, and F. G. Deng, Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED, Sci. Rep. 5(1), 9274 (2015)CrossRefGoogle Scholar
  64. 64.
    B. Ye, Z. F. Zheng, Y. Zhang, C. P. Yang, and Q. E. D. Circuit, single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n — 1 microwave photonic qubits, Opt. Express 26(23), 30689 (2018)ADSCrossRefGoogle Scholar
  65. 65.
    M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, Synthesizing arbitrary quantum states in a superconducting resonator, Nature 459(7246), 546 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, Generation of Fock states in a superconducting quantum circuit, Nature 454(7202), 310 (2008)ADSCrossRefGoogle Scholar
  67. 67.
    H. Wang, M. Hofheinz, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, A. N. Cleland, and J. M. Martinis, Measurement of the decay of Fock states in a superconducting quantum circuit, Phys. Rev. Lett. 101(24), 240401 (2008)ADSCrossRefGoogle Scholar
  68. 68.
    Y. Xu, W. Cai, Y. Ma, X. Mu, W. Dai, W. Wang, L. Hu, X. Li, J. Han, H. Wang, Y. Song, Z. B. Yang, S. B. Zheng, and L. Sun, Geometrically manipulating photonic Schrödinger cat states and realizing cavity phase gates, arXiv: 1810.04690 (2018)Google Scholar
  69. 69.
    H. Wang, M. Mariantoni, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, T. Yamamoto, Y. Yin, J. Zhao, J. M. Martinis, and A. N. Cleland, Deterministic entanglement of photons in two superconducting microwave resonators, Phys. Rev. Lett. 106(6), 060401 (2011)ADSCrossRefGoogle Scholar
  70. 70.
    M. Mariantoni, H. Wang, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, T. Yamamoto, Y. Yin, J. Zhao, J. M. Martinis, and A. N. Cleland, Photon shell game in three-resonator circuit quantum electrodynamics, Nat. Phys. 7(4), 287 (2011)CrossRefGoogle Scholar
  71. 71.
    L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C. L. Zou, S. M. Girvin, L. M. Duan, and L. Sun, Quantum error correction and universal gate set operation on a binomial bosonic logical qubit., Nat. Phys. 15(5), 503 (2019)CrossRefGoogle Scholar
  72. 72.
    R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a universal gate set on a logical qubit encoded in an oscillator, Nat. Commun. 8(1), 94 (2017)ADSCrossRefGoogle Scholar
  73. 73.
    N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Extending the lifetime of a quantum bit with error correction in superconducting circuits, Nature 536(7617), 441 (2016)ADSCrossRefGoogle Scholar
  74. 74.
    C. P. Yang and Z. F. Zheng, Deterministic generation of Greenberger-Horne-Zeilinger entangled states of cat-state qubits in circuit QED, Opt. Lett. 43(20), 5126 (2018)ADSCrossRefGoogle Scholar
  75. 75.
    M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: A new paradigm for universal quantum computation, New J. Phys. 16(4), 045014 (2014)ADSCrossRefGoogle Scholar
  76. 76.
    S. E. Nigg, Deterministic Hadamard gate for microwave cat-state qubits in circuit QED, Phys. Rev. A 89(2), 022340 (2014)ADSCrossRefGoogle Scholar
  77. 77.
    Y. Zhang, X. Zhao, Z. F. Zheng, L. Yu, Q. P. Su, and C. P. Yang, Universal controlled-phase gate with cat-state qubits in circuit QED, Phys. Rev. A 96(5), 052317 (2017)ADSCrossRefGoogle Scholar
  78. 78.
    Y. J. Fan, Z. F. Zheng, Y. Zhang, D. M. Lu, and C. P. Yang, One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED, Front. Phys. 14(2), 21602 (2019)CrossRefGoogle Scholar
  79. 79.
    R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a universal gate set on a logical qubit encoded in an oscillator, Nat. Commun. 8(1), 94 (2017)ADSCrossRefGoogle Scholar
  80. 80.
    C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, A Schrodinger cat living in two boxes, Science 352(6289), 1087 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  81. 81.
    P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, Using sideband transitions for two-qubit operations in superconducting circuits, Phys. Rev. B 79(18), 180511 (2009)ADSCrossRefGoogle Scholar
  82. 82.
    M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Tuning the field in a microwave resonator faster than the photon lifetime, Appl. Phys. Lett. 92(20), 203501 (2008)ADSCrossRefGoogle Scholar
  83. 83.
    D. F. V. James and J. Jerke, Effective Hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)ADSCrossRefGoogle Scholar
  84. 84.
    J. Q. You, X. Hu, S. Ashhab, and F. Nori, Low-decoherence flux qubit, Phys. Rev. B 75, 140515(R) (2007)ADSCrossRefGoogle Scholar
  85. 85.
    M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, High-coherence hybrid superconducting qubit, Phys. Rev. Lett. 105(10), 100502 (2010)ADSCrossRefGoogle Scholar
  86. 86.
    F. Yan, S. Gustavsson, A. Kamal, J. Birenbaum, A. P. Sears, D. Hover, T. J. Gudmundsen, D. Rosenberg, G. Samach, S. Weber, J. L. Yoder, T. P. Orlando, J. Clarke, A. J. Kerman, and W. D. Oliver, The flux qubit revisited to enhance coherence and reproducibility, Nat. Commun. 7(1), 12964 (2016)ADSCrossRefGoogle Scholar
  87. 87.
    M. Baur, S. Filipp, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, P. J. Leek, A. Blais, and A. Wallraff, Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit, Phys. Rev. Lett. 102(24), 243602 (2009)ADSCrossRefGoogle Scholar
  88. 88.
    F. Yoshihara, Y. Nakamura, F. Yan, S. Gustavsson, J. Bylander, W. D. Oliver, and J. S. Tsai, Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions, Phys. Rev. B 89(2), 020503 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  • Tong Liu
    • 1
  • Zhen-Fei Zheng
    • 2
  • Yu Zhang
    • 3
  • Yu-Liang Fang
    • 1
  • Chui-Ping Yang
    • 1
    Email author
  1. 1.Quantum Information Research CenterShangrao Normal UniversityShangraoChina
  2. 2.Key Laboratory of Quantum InformationUniversity of Science and Technology of ChinaHeifeiChina
  3. 3.School of PhysicsNanjing UniversityNanjingChina

Personalised recommendations