Advertisement

Frontiers of Physics

, 14:21602 | Cite as

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

  • You-Ji Fan
  • Zhen-Fei Zheng
  • Yu Zhang
  • Dao-Ming Lu
  • Chui-Ping YangEmail author
Research Article
  • 11 Downloads

Abstract

We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit (cqubit) simultaneously controlling n–1 target cqubits. The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.

Keywords

circuit QED cat-state multi-target-qubit controlled phase gate 

Notes

Acknowledgements

This work was supported in part by the NKRDP of China (Grant No. 2016YFA0301802) and the National Natural Science Foundation of China under Grant Nos. 11074062, 11374083, and 11774076. This work was also supported by the Hangzhou-City grant for Quantum Information and Quantum Optics Innovation Research Team.

References

  1. 1.
    D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. Lond. A 400(1818), 97 (1985)ADSMathSciNetzbMATHGoogle Scholar
  2. 2.
    P. W. Shor, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science IEEE Computer Society Press, Santa Fe, NM, 1994Google Scholar
  3. 3.
    L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79(2), 325 (1997)ADSGoogle Scholar
  4. 4.
    A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52(5), 3457 (1995)ADSGoogle Scholar
  5. 5.
    M. Mötöen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, Quantum circuits for general multiqubit gates, Phys. Rev. Lett. 93(13), 130502 (2004)Google Scholar
  6. 6.
    Y. Liu, G. L. Long, and Y. Sun, Analytic one-bit and CNOT gate constructions of general n-qubit controlled gates, Int. J. Quant. Inf. 6(03), 447 (2008)zbMATHGoogle Scholar
  7. 7.
    J. K. Pachos and P. L. Knight, Quantum computation with a one-dimensional optical lattice, Phys. Rev. Lett. 91(10), 107902 (2003)ADSGoogle Scholar
  8. 8.
    H. Ollivier and P. Milman, Proposal for realization of a Toffoli gate via cavity-assisted collision, arXiv: quantph/0306064 (2003)zbMATHGoogle Scholar
  9. 9.
    J. Zhang, W. Liu, Z. Deng, Z. Lu, and G. L. Long, Modularization of multi-qubit controlled phase gate and its NMR implementation, J. Opt. B 7, 22 (2005)ADSGoogle Scholar
  10. 10.
    A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481(7380), 170 (2012)ADSGoogle Scholar
  11. 11.
    L. M. Duan, B. Wang, and H. J. Kimble, Robust quantum gates on neutral atoms with cavity-assisted photonscattering, Phys. Rev. A 72(3), 032333 (2005)ADSGoogle Scholar
  12. 12.
    X. Wang, A. Sørensen, and K. Mølmeret, Multibit gates for quantum computing, Phys. Rev. Lett. 86(17), 3907 (2001)ADSGoogle Scholar
  13. 13.
    X. Zou, Y. Dong, and G. C. Guo, Implementing a conditional z gate by a combination of resonant interaction and quantum interference, Phys. Rev. A 74(3), 032325 (2006)ADSGoogle Scholar
  14. 14.
    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)ADSGoogle Scholar
  15. 15.
    C. P. Yang and S. Han, Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED, Phys. Rev. A 73(3), 032317 (2006)ADSGoogle Scholar
  16. 16.
    W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, One-step implementation of multi-qubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity, Appl. Phys. Lett. 96(24), 241113 (2010)ADSGoogle Scholar
  17. 17.
    S. B. Zheng, Implementation of Toffoli gates with a single asymmetric Heisenberg XY interaction, Phys. Rev. A 87(4), 042318 (2013)ADSGoogle Scholar
  18. 18.
    T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett. 102(4), 040501 (2009)ADSGoogle Scholar
  19. 19.
    H. R. Wei and F. G. Deng, Universal quantum gates for hybrid systems assisted by quantum dots inside doublesided optical microcavities, Phys. Rev. A 87(2), 022305 (2013)ADSGoogle Scholar
  20. 20.
    H. W. Wei and F. G. Deng, Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities, Sci. Rep. 4(1), 7551 (2014)Google Scholar
  21. 21.
    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)ADSGoogle Scholar
  22. 22.
    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)Google Scholar
  23. 23.
    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)ADSGoogle Scholar
  24. 24.
    C. P. Yang, S. B. Zheng, and F. Nori, Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity, Phys. Rev. A 82(6), 062326 (2010)ADSGoogle Scholar
  25. 25.
    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)ADSGoogle Scholar
  26. 26.
    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)ADSGoogle Scholar
  27. 27.
    T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, Multi-target-qubit unconventional geometric phase gate in a multicavity system, Sci. Rep. 6(1), 21562 (2016)ADSGoogle Scholar
  28. 28.
    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)ADSGoogle Scholar
  29. 29.
    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)ADSGoogle Scholar
  30. 30.
    S. E. Nigg, Deterministic hadamard gate for microwave cat-state qubits in circuit QED, Phys. Rev. A 89(2), 022340 (2014)ADSGoogle Scholar
  31. 31.
    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)ADSGoogle Scholar
  32. 32.
    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, arXiv: 1608.02430 (2016)Google Scholar
  33. 33.
    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 Schrödinger cat living in two boxes, Science 352(6289), 1087 (2016)ADSMathSciNetzbMATHGoogle Scholar
  34. 34.
    C. P. Yang, S. I. Chu, and S. Han, Possible realization of entanglement, logical gates, and quantuminformation transfer with superconducting-quantuminterference-device qubits in cavity QED, Phys. Rev. A 67(4), 042311 (2003)ADSGoogle Scholar
  35. 35.
    J. Q. You and F. Nori, Quantum information processing with superconducting qubits in a microwave field, Phys. Rev. B 68(6), 064509 (2003)ADSGoogle Scholar
  36. 36.
    A. Blais, R. S. Huang, A. Wallra, 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)ADSGoogle Scholar
  37. 37.
    J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58(11), 42 (2005)Google Scholar
  38. 38.
    J. Clarke and F. K. Wilhelm, Superconducting quantum bits, Nature 453(7198), 1031 (2008)ADSGoogle Scholar
  39. 39.
    J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011)ADSGoogle Scholar
  40. 40.
    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)ADSGoogle Scholar
  41. 41.
    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)MathSciNetzbMATHGoogle Scholar
  42. 42.
    M. AbuGhanem, A. H. Homid, and M. Abdel-Aty, Cavity control as a new quantum algorithms implementation treatment, Front. Phys. 13, 130303 (2018)Google Scholar
  43. 43.
    H. P. Cui, Y. Shan, J. Zou, and B. Shao, Entanglement reciprocation between two charge qubits and cavity field, Front. Phys. China 3, 258 (2008)ADSGoogle Scholar
  44. 44.
    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. Applied 4, 044003 (2015)ADSGoogle Scholar
  45. 45.
    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, 012318 (2012)ADSGoogle Scholar
  46. 46.
    M. Šašura and V. Buzek, Multiparticle entanglement with quantum logic networks: Application to cold trapped ions, Phys. Rev. A 64(1), 012305 (2001)ADSGoogle Scholar
  47. 47.
    F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing, CRC Press, USA, 2008zbMATHGoogle Scholar
  48. 48.
    T. Beth and M. Rötteler, Quantum Information, Springer, Berlin, 2001, Vol. 173, Ch. 4, p. 96ADSGoogle Scholar
  49. 49.
    S. L. Braunstein, V. Buzek, and M. Hillery, Quantuminformation distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit, Phys. Rev. A 63(5), 052313 (2001)ADSGoogle Scholar
  50. 50.
    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76(4), 042319 (2007)ADSGoogle Scholar
  51. 51.
    D. Sank, Z. Chen, M. Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, A. Vainsencher, T. White, J. Wenner, A. N. Korotkov, and J. M. Martinis, Measurement-induced state transitions in a superconducting qubit: beyond the rotating wave approximation, Phys. Rev. Lett. 117(19), 190503 (2016)ADSMathSciNetGoogle Scholar
  52. 52.
    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)ADSGoogle Scholar
  53. 53.
    R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O’Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and J. M. Martinis, Coherent Josephson qubit suitable for scalable quantum integrated circuits, Phys. Rev. Lett. 111(8), 080502 (2013)ADSGoogle Scholar
  54. 54.
    M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, and J. M. Martinis, Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state, Nat. Phys. 4(7), 523 (2008)Google Scholar
  55. 55.
    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)ADSGoogle Scholar
  56. 56.
    Z. L. Wang, Y. P. Zhong, L. J. He, H. Wang, J. M. Martinis, A. N. Cleland, and Q. W. Xie, Quantum state characterization of a fast tunable superconducting resonator, Appl. Phys. Lett. 102(16), 163503 (2013)ADSGoogle Scholar
  57. 57.
    D. F. James and J. Jerke, Effective hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)ADSGoogle Scholar
  58. 58.
    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)ADSGoogle Scholar
  59. 59.
    C. P. Yang, Q. P. Su, S. B. Zheng, and S. Han, One-step transfer or exchange of arbitrary multipartite quantum states with a single-qubit coupler, Phys. Rev. B 92(5), 054509 (2015)ADSGoogle Scholar
  60. 60.
    Y. X. Liu, S. K. Özdemir, A. Miranowicz, and N. Imoto, Kraus representation of a damped harmonic oscillator and its application, Phys. Rev. A 70, 042308 (2004)ADSGoogle Scholar
  61. 61.
    C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, Crosstalkinsensitive method for simultaneously coupling multiple pairs of resonators, Phys. Rev. A 93(4), 042307 (2016)ADSGoogle Scholar
  62. 62.
    J. A. Schreier, A. A. Houck, J. Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Suppressing charge noise decoherence in superconducting charge qubits, Phys. Rev. B 77, 180502(R) (2008)ADSGoogle Scholar
  63. 63.
    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)Google Scholar
  64. 64.
    For a transmon qutrit, the |g〉 ↔ |f〉 transition is much weaker than those of the |g〉 ↔ |e〉 and |e〉 ↔ |f〉 transitions. Thus, we have γfg –1 » γeg –1, γfe –1.Google Scholar
  65. 65.
    C. Rigetti, S. Poletto, J. M. Gambetta, B. L. T. Plourde, J. M. Chow, et al., Superconducting qubit in waveguide cavity with coherence time approaching 0.1 ms, Phys. Rev. B 86, 100506(R) (2012)ADSGoogle Scholar
  66. 66.
    M. J. Peterer, S. J. Bader, X. Jin, F. Yan, A. Kamal, T. J. Gudmundsen, P. J. Leek, T. P. Orlando, W. D. Oliver, and S. Gustavsson, Coherence and decay of higher energy levels of a superconducting transmon qubit, Phys. Rev. Lett. 114, 010501 (2015)ADSGoogle Scholar
  67. 67.
    A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481, 170 (2011)ADSGoogle Scholar
  68. 68.
    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)ADSGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • You-Ji Fan
    • 1
  • Zhen-Fei Zheng
    • 2
  • Yu Zhang
    • 3
  • Dao-Ming Lu
    • 1
  • Chui-Ping Yang
    • 4
    • 5
    Email author
  1. 1.College of Mechanic and Electronic EngineeringWuyi UniversityWuyishanChina
  2. 2.CAS Key Laboratory of Quantum InformationUniversity of Science and Technology of ChinaHefeiChina
  3. 3.School of PhysicsNanjing UniversityNanjingChina
  4. 4.Quantum Information Research CenterShangrao Normal UniversityShangraoChina
  5. 5.Department of PhysicsHangzhou Normal UniversityHangzhouChina

Personalised recommendations