Skip to main content
SpringerLink
Log in

One-step implementation of a Toffoli gate of separated superconducting qubits via quantum Zeno dynamics

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Based on the quantum Zeno dynamics, a scheme is presented to implement a Toffoli gate of three separated superconducting qubits (SQs) by one step. Three separated SQs are connected by two resonators. The scheme is insensitive to the resonator decay because the Zeno subspace does not include the state of the resonators being excited. Numerical simulations indicate that the scheme is robust to the fluctuation of the parameters and the Toffoli gate can be implemented with high fidelity.

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. Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature (London) 409, 46–52 (2001)

    Article  ADS  MATH  Google Scholar 

  2. Beenakker, C.W.J., Divincenzo, D.P., Emary, C., Kindrmann, M.: Charge detection enables free-electron quantum computation. Phys. Rev. Lett. 93, 020501 (2004)

    Article  ADS  Google Scholar 

  3. Ren, B.C., Wei, H.R., Deng, F.G.: Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity. Laser Phys. Lett. 10, 095202 (2013)

    Article  ADS  Google Scholar 

  4. Feng, G.R., Xu, G.F., Lang, G.L.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013)

    Article  ADS  Google Scholar 

  5. Hu, C.Y., Munro, W.J., Rarity, J.G.: Deterministic photon entangler using a charged quantum dot inside a microcavity. Phys. Rev. B 78, 125318 (2008)

    Article  ADS  Google Scholar 

  6. Xu, G.F., Zhang, J., Tong, D.M., Sj\(\ddot{o}\)qvist, E., Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109, 170501 (2012)

  7. Togan, E., Chu, Y., Trifonov, A.S., Jiang, L., Maze, J., Childress, L., Dutt, M.V.G., Sørensen, A.S., Hemmer, P.R., Zibrov, A.S., Lukin, M.D.: Quantum entanglement between an optical photon and a solid-state spin qubit. Nature (London) 466, 730–734 (2010)

    Article  ADS  Google Scholar 

  8. Osnaghi, S., Bertet, P., Auffeves, A., Maioli, P., Brune, M., Raimond, J.M., Haroche, S.: Coherent control of an atomic collision in a cavity. Phys. Rev. Lett. 87, 037902 (2001)

    Article  ADS  Google Scholar 

  9. Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., Haroche, S.: Step-by-step engineered multiparticle entanglement. Science 288, 2024–2028 (2000)

    Article  ADS  Google Scholar 

  10. Lucero, E., Barends, R., Chen, Y., Kelly, J., Mariantoni, M., Megrant, A., O’Malley, P., Sank, D., Vainsencher, A., Wenner, J., White, T., Yin, Y., Cleland, A.N., Martinis, J.M.: Computing prime factors with a Josephson phase qubit quantum processor. Nat. Phys. 8, 719–723 (2012)

    Article  Google Scholar 

  11. Rigetti, C., Gambetta, J.M., Poletto, S., Plourde, B.L.T., Chow, J.M., Córcoles, A.D., Smolin, J.A., Merkel, S.T., Rozen, J.R., Keefe, G.A., Rothwell, M.B., Ketchen, M.B., Steffen, M.: Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms. Phys. Rew. B 86, 100506(R) (2012)

    Article  ADS  Google Scholar 

  12. You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature (London) 474, 589–597 (2011)

    Article  ADS  Google Scholar 

  13. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.S., Majer, J., Kumar, S., Girvin, S.M., Schoelkopf, R.J.: Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature (London) 431, 162–167 (2004)

    Article  ADS  Google Scholar 

  14. Chiorescu, I., Bertet, P., Semba, K., Nakamura, Y., Harmans, C.J.P.M., Mooij, J.E.: Coherent dynamics of a flux qubit coupled to a harmonic oscillator. Nature (London) 431, 159–162 (2004)

    Article  ADS  Google Scholar 

  15. Harris, R., Berkley, A.J., Johnson, M.W., Bunyk, P., Govorkov, S., Thom, M.C., Uchaikin, S., Wilson, A.B., Chung, J., Holtham, E., Biamonte, J.D., Smirnov, A.Y., Amin, M.H.S., van den Brink, A.M.: Sign-and magnitude-tunable coupler for superconducting flux qubits. Phys. Rev. Lett. 98, 177001 (2007)

    Article  ADS  Google Scholar 

  16. Srinivasan, S.J., Hoffman, A.J., Gambetta, J.M., Houck, A.A.: Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a V-shaped energy level diagram. Phys. Rev. Lett. 106, 083601 (2011)

    Article  ADS  Google Scholar 

  17. Leek, P.J., Filipp, S., Maurer, P., Baur, M., Bianchetti, R., Fink, J.M., G\(\ddot{o}\)pp, M., Steffen, L., Wallraff, A.: Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79, 180511(R) (2009)

  18. DiCarlo, L., Reed, M.D., Sun, L., Johnson, B.R., Chow, J.M., Gambetta, J.M., Frunzio, L., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature (London) 467, 574–578 (2010)

    Article  ADS  Google Scholar 

  19. Neeley, M., Bialczak, R.C., Lenander, M., Lucero, E., Mariantoni, M., O’Connell, A.D., Sank, D., Wang, H., Weides, M., Wenner, J., Yin, Y., Yamamoto, T., Cleland, A.N., Martinis, J.M.: Generation of three-qubit entangled states using superconducting phase qubits. Nature (London) 467, 570–573 (2010)

    Article  ADS  Google Scholar 

  20. Fedorov, A., Steffen, L., Baur, M., da Silva, M.P., Wallraff, A.: Implementation of a Toffoli gate with superconducting circuits. Nature (London) 481, 170–172 (2011)

    Article  ADS  Google Scholar 

  21. Reed, M.D., DiCarlo, L., Nigg, S.E., Sun, L., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Realization of three-qubit quantum error correction with superconducting circuits. Nature (London) 482, 382–385 (2012)

    Article  ADS  Google Scholar 

  22. Barends, R., Kelly, J., Megrant, A., Veitia, A., Sank, D., Jeffrey, E., White, T.C., Mutus, J., Fowler, A.G., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Neill, C., O’Malley, P., Roushan, P., Vainsencher, A., Wenner, J., Korotkov, A.N., Cleland, A.N., Martinis, J.M.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature (London) 508, 500–503 (2014)

    Article  ADS  Google Scholar 

  23. Strauch, F.W., Jacobs, K., Simmonds, R.W.: Arbitrary control of entanglement between two superconducting resonators. Phys. Rev. Lett. 105, 050501 (2010)

    Article  ADS  Google Scholar 

  24. Merkel, S.T., Wilhelm, F.K.: Generation and detection of NOON states in superconducting circuits. New J. Phys. 12, 093036 (2010)

    Article  ADS  Google Scholar 

  25. Yang, C.P., Su, Q.P., Han, S.: 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, 022329 (2012)

    Article  ADS  Google Scholar 

  26. 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 

  27. Hua, M., Tao, M.J., Deng, F.G.: Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics. Phys. Rev. A 90, 012328 (2014)

    Article  ADS  Google Scholar 

  28. Wang, H., Mariantoni, M., Bialczak, R.C., Lenander, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Weides, M., Wenner, J., Yamamoto, T., Yin, Y., Zhao, J., Martinis, J.M., Cleland, A.N.: Deterministic entanglement of photons in two superconducting microwave resonators. Phys. Rev. Lett. 106, 060401 (2011)

    Article  ADS  Google Scholar 

  29. Mariantoni, M., Wang, H., Bialczak, R.C., Lenander, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Weides, M., Wenner, J., Yamamoto, T., Yin, Y., Zhao, J., Martinis, J.M., Cleland, A.N.: Photon shell game in three-resonator circuit quantum electrodynamics. Nat. Phys. 7, 287–293 (2011)

    Article  Google Scholar 

  30. Sillanpää, M.A., Park, J.I., Simmonds, R.W.: Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature (London) 449, 438–442 (2007)

    Article  ADS  Google Scholar 

  31. Majer, J., Chow, J.M., Gambetta, J.M., Koch, J., Johnson, B.R., Schreier, J.A., Frunzio, L., Schuster, D.I., Houck, A.A., Wallraff, A., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Coupling superconducting qubits via a cavity bus. Nature (London) 449, 443–447 (2007)

    Article  ADS  Google Scholar 

  32. Chen, C.Y., Feng, M., Gao, K.L.: Toffoli gate originating from a single resonant interaction with cavity QED. Phys. Rev. A 73, 064304 (2006)

    Article  ADS  Google Scholar 

  33. Shao, X.Q., Zhu, A.D., Zhang, S., Chung, J.S., Yeon, K.H.: Efficient scheme for implementing an N-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics. Phys. Rev. A 75, 034307 (2007)

    Article  ADS  Google Scholar 

  34. Palph, T.C., Resch, K.J., Gilchrist, A.: Efficient Toffoli gates using qudits. Phys. Rev. A 75, 022313 (2007)

    Article  ADS  Google Scholar 

  35. Tame, M.S., Özdemir, S.K., Koashi, M., Imoto, N., Kim, M.S.: Compact Toffoli gate using weighted graph states. Phys. Rev. A 79, 020302(R) (2009)

    Article  ADS  Google Scholar 

  36. Shao, X.Q., Wang, H.F., Chen, L., Zhang, S., Yeon, K.H.: One-step implementation of the Toffoli gate via quantum Zeno dynamics. Phys. Lett. A 374, 28–33 (2009)

    Article  ADS  MATH  Google Scholar 

  37. Cory, D.G., Price, M.D., Maas, W., Knill, E., Laflamme, R., Zurek, W.H., Havel, T.F., Somaroo, S.S.: Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)

    Article  ADS  Google Scholar 

  38. Monz, T., Kim, K.: H\(\ddot{a}\)nsel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., Blatt, R.: Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102, 040501 (2009)

  39. Misra, B., Sudarshan, E.C.G.: The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756–763 (1977)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Beige, A., Braun, D., Tregenna, B., Knight, P.L.: Quantum computing using dissipation to remain in a decoherence-free subspace. Phys. Rev. Lett. 85, 1762–1765 (2000)

    Article  ADS  Google Scholar 

  42. Pachos, J.K., Beige, A.: Decoherence-free dynamical and geometrical entangling phase gates. Phys. Rev. A 69, 033817 (2004)

    Article  ADS  Google Scholar 

  43. Li, W.A., Huang, G.Y.: Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics. Phys. Rev. A 83, 022322 (2011)

    Article  ADS  Google Scholar 

  44. Shen, L.T., Wu, H.Z., Chen, R.X.: Robust generation of a four-dimensional entangled state in separate cavities via quantum Zeno dynamics. J. Phys. B At. Mol. Opt. Phys. 44, 205503 (2011)

    Article  ADS  Google Scholar 

  45. Raimond, J.M., Sayrin, C., Gleyzes, S., Dotsenko, I., Brune, M., Haroche, S., Facchi, P., Pascazio, S.: Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics. Phys. Rev. Lett. 105, 213601 (2010)

    Article  ADS  Google Scholar 

  46. Raimond, J.M., Facchi, P., Peaudecerf, B., Pascazio, S., Sayrin, C., Dotsenko, I., Gleyzes, S., Brune, M., Haroche, S.: Quantum Zeno dynamics of a field in a cavity. Phys. Rev. A 86, 032120 (2012)

    Article  ADS  Google Scholar 

  47. Signoles, A., Facon, A., Grosso, D., Dotsenko, L., Haroche, S., Raimond, J.M., Bruneand, M., Gleyzes, S.: Confined quantum Zeno dynamics of a watched atomic arrow. Nat. Phys. 10, 715–719 (2014)

    Article  Google Scholar 

  48. Schafer, F., Herrera, I., Cherukattil, S., Lovecchio, C., Cataliotti, F.S., Caruso, F., Smerzi, A.: Experimental realization of quantum zeno dynamics. Nat. Commun. 5, 3194 (2014)

    Article  ADS  Google Scholar 

  49. Bretheau, L., Campagne-Ibareq, P., Flurin, E., Mallet, F., Huard, B.: Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 348, 776–779 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  50. Zahedinejad, E., Ghosh, J., Sanders, B.C.: High-fidelity single-shot Toffoli gate via quantum control. Phys. Rev. Lett. 114, 200502 (2015)

    Article  ADS  Google Scholar 

  51. Wei, L.F., Liu, Y.X., Nori, F.: Generation and control of Greenberger–Horne–Zeilinger entanglement in superconducting circuits. Phys. Rev. Lett. 96, 246803 (2006)

    Article  ADS  Google Scholar 

  52. Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., Garcia-Ripoll, J.J., Zueco, D., Hummer, T., Solano, E., Marx, A., Gross, R.: Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nat. Phys. 6, 772–776 (2010)

    Article  Google Scholar 

  53. Schuster, D.I., Sears, A.P., Ginossar, E., DiCarlo, L., Frunzio, L., Morton, J.J.L., Wu, H., Briggs, G.A.D., Buckley, B.B., Awschalom, D.D., Schoelkopf, R.J.: High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010)

    Article  ADS  Google Scholar 

  54. Feng, Z.B., Zhang, X.D.: Holonomic quantum computation with superconducting charge-phase qubits in a cavity. Phys. Lett. A 372, 1589–1594 (2008)

    Article  ADS  MATH  Google Scholar 

  55. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Majer, J., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the funds from the National Natural Science Foundation of China under Grant No.11374054.

Author information

Authors and Affiliations

  1. College of Physics and Information Engineering, Fuzhou University, Fuzhou, 350002, China

    Mei-Feng Chen, Yong-Fa Chen & Song-She Ma

Authors
  1. Mei-Feng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong-Fa Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Song-She Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mei-Feng Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, MF., Chen, YF. & Ma, SS. One-step implementation of a Toffoli gate of separated superconducting qubits via quantum Zeno dynamics. Quantum Inf Process 15, 1469–1483 (2016). https://doi.org/10.1007/s11128-015-1222-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1222-7

Keywords

Search

Navigation