Abstract
An efficient method is proposed for the generation and swapping of multi-qubit entangled state in an array of linearly coupled superconducting resonators, each of which is coupled to N superconducting qubits. With the external driving fields to adjust the desired qubit–resonator interaction, we firstly show that the multipartite entangled state of superconducting qubits hosted in two nearest-neighbor interacting resonators can be deterministically realized. Furthermore, by utilizing the produced entangled state, we put forward a protocol for the swapping of quantum entangled state in the coupled resonator array based on measurement, i.e., the multi-particle entangled state can be achieved for the qubits in long-distance separated resonators. The numerical simulation suggests that our scheme is feasible with current circuit QED technology.



Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature (London) 474, 589 (2011)
Yang, C.P., Chu, S.I., Han, S.: Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity qed. Phys. Rev. A 67, 042311 (2003)
You, J.Q., Nori, F.: Quantum information processing with superconducting qubits in a microwave field. Phys. Rev. B 68, 064509 (2003)
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 (2007)
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 (2007)
Blais, A., Huang, R.S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)
Yang, C.P., Chu, S.I., Han, S.: 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, 117902 (2004)
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 (2004)
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 (2004)
Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)
Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996)
Knill, E.: Quantum computing with realistically noisy devices. Nature (London) 434, 39 (2005)
Lloyd, S.: Universal quantum simulators. Science 273, 1073 (1996)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Vaidman, L.: Teleportation of quantum states. Phys. Rev. A 49, 1473 (1994)
Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell theorem without inequalities. Am. J. Phys. 58, 1131 (1990)
Ansmann, M., Wang, H., Bialczak, R.C., Hofheinz, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Weides, M., Wenner, J., Cleland, A.N., Martinis, J.M.: Violation of bell’s inequality in Josephson phase qubits. Nature (London) 461, 504 (2009)
Leggett, A.J.: Realism and the physical world. Rep. Prog. Phys. 71, 022001 (2008)
Steffen, M., Ansmann, M., Bialczak, R.C., Katz, N., Lucero, E., McDermott, R., Neeley, M., Weig, E.M., Cleland, A.N., Martinis, J.M.: Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423 (2006)
DiCarlo, L., Chow, J.M., Gambetta, J.M., Bishop, L.S., Johnson, B.R., Schuster, D.I., Majer, J., Blais, A., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature (London) 460, 240 (2009)
Yamamoto, T., Pashkin, Y.A., Astafiev, O., Nakamura, Y., Tsai, J.S.: Demonstration of conditional gate operation using superconducting charge qubits. Nature (London) 425, 941 (2003)
Hime, T., Reichardt, P.A., Plourde, B.L.T., Robertson, T.L., Wu, C.E., Ustinov, A.V., Clarke, J.: Solid-state qubits with current-controlled coupling. Science 314, 1427 (2006)
van der Ploeg, S.H.W., Izmalkov, A., van den Brink, A.M., Hübner, U., Grajcar, M., Il’ichev, E., Meyer, H.G., Zagoskin, A.M.: Controllable coupling of superconducting flux qubits. Phys. Rev. Lett. 98, 057004 (2007)
Ristè, D., Dukalski, M., Watson, C.A., de Lange, G., Tiggelman, M.J., Blanter, Y.M., Lehnert, K.W., Schouten, R.N., DiCarlo, L.: Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature (London) 502, 350 (2013)
Barends, R., et al.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature (London) 508, 500 (2014)
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 (2010)
Neeley, M., Bialczak, R.C., Lenander, M., Lucero, E., Mariantoni, M., Oonnell, 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 (2010)
Zhong, Y.P., Xu, D., Wang, P., Song, C., Guo, Q.J., Liu, W.X., Xu, K., Xia, B.X., Lu, C.Y., Han, S., Pan, J.W., Wang, H.: Emulating anyonic fractional statistical behavior in a superconducting quantum circuit. Phys. Rev. Lett. 117, 110501 (2016)
Paik, H., Mezzacapo, A., Sandberg, M., McClure, D.T., Abdo, B., Córcoles, A.D., Dial, O., Bogorin, D.F., Plourde, B.L.T., Steffen, M., Cross, A.W., Gambetta, J.M., Chow, J.M.: Experimental demonstration of a resonator-induced phase gate in a multiqubit circuit-qed system. Phys. Rev. Lett. 117, 250502 (2016)
Deng, Z.J., Gao, K.L., Feng, M.: Generation of \(n\)-qubit \(w\) states with rf squid qubits by adiabatic passage. Phys. Rev. A 74, 064303 (2006)
Song, K.H., Xiang, S.H., Liu, Q., Lu, D.H.: Quantum computation and \(w\)-state generation using superconducting flux qubits coupled to a cavity without geometric and dynamical manipulation. Phys. Rev. A 75, 032347 (2007)
Yang, C.P.: Preparation of \(n\)-qubit Greenberger–Horne–Zeilinger entangled states in cavity qed: an approach with tolerance to nonidentical qubit-cavity coupling constants. Phys. Rev. A 83, 062302 (2011)
Yang, Zp, Li, Z., Ma, Sl, Li, Fl: One-step generation of continuous-variable quadripartite cluster states in a circuit qed system. Phys. Rev. A 96, 012327 (2017)
Song, C., Xu, K., Liu, W., Yang, Cp, Zheng, S.B., Deng, H., Xie, Q., Huang, K., Guo, Q., Zhang, L., Zhang, P., Xu, D., Zheng, D., Zhu, X., Wang, H., Chen, Y.A., Lu, C.Y., Han, S., Pan, J.W.: 10-qubit entanglement and parallel logic operations with a superconducting circuit. Phys. Rev. Lett. 119(2), 180511 (2017)
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)
Ma, S.L., Li, Z., Fang, A.P., Li, P.B., Gao, S.Y., Li, F.L.: Controllable generation of two-mode-entangled states in two-resonator circuit qed with a single gap-tunable superconducting qubit. Phys. Rev. A 90, 062342 (2014)
You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58, 42 (2005)
Sandberg, M., Wilson, C.M., Persson, F., Bauch, T., Johansson, G., Shumeiko, V., Duty, T., Delsing, P.: Tuning the field in a microwave resonator faster than the photon lifetime. Appl. Phys. Lett. 92, 203501 (2008)
Nation, P.D., Blencowe, M.P., Rimberg, A.J., Buks, E.: Analogue hawking radiation in a dc-squid array transmission line. Phys. Rev. Lett. 103, 087004 (2009)
Felicetti, S., Sanz, M., Lamata, L., Romero, G., Johansson, G., Delsing, P., Solano, E.: Dynamical Casimir effect entangles artificial atoms. Phys. Rev. Lett. 113, 093602 (2014)
Paauw, F.G., Fedorov, A., Harmans, C.J.P.M., Mooij, J.E.: Tuning the gap of a superconducting flux qubit. Phys. Rev. Lett. 102, 090501 (2009)
Mooij, J.E., Orlando, T.P., Levitov, L., Tian, L., van der Wal, C.H., Lloyd, S.: Josephson persistent-current qubit. Science 285, 1036 (1999)
Orlando, T.P., Mooij, J.E., Tian, L., van der Wal, C.H., Levitov, L.S., Lloyd, S., Mazo, J.J.: Superconducting persistent-current qubit. Phys. Rev. B 60, 15398 (1999)
Strand, J.D., et al.: First-order sideband transitions with flux-driven asymmetric transmon qubits. Phys. Rev. B 87, 220505(R) (2013)
Wu, Yulin, et.al.: An efficient and compact quantum switch for quantum circuits. arXiv:1605.06747 (2016)
Chen, Zhen, et al.: Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit-quantum-electrodynamics system. Phys. Rev. A 96, 012325 (2017)
Ma, Sl, Li, Pb, Fang, Ap, Gao, Sy, Li, Fl: Dissipation-assisted generation of steady-state single-mode squeezing of collective excitations in a solid-state spin ensemble. Phys. Rev. A 88, 013837 (2013)
Wallraff, A., et al.: Sideband transitions and two-tone spectroscopy of a superconducting qubit strongly coupled to an on-chip cavity. Phys. Rev. Lett. 99, 050501 (2007)
Sørensen, A., Mølmer, K.: Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62, 022311 (2000)
Zheng, S.B.: Quantum-information processing and multiatom-entanglement engineering with a thermal cavity. Phys. Rev. A 66, 060303 (2002)
Mølmer, K., Sørensen, A.: Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 82, 1835 (1999)
Wang, Y.D., Chesi, S., Loss, D., Bruder, C.: One-step multiqubit Greenberger–Horne–Zeilinger state generation in a circuit qed system. Phys. Rev. B 81, 104524 (2010)
Żukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)
Zhang, Z.-J., Man, Z.-X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)
Hime, T., Reichardt, P.A., Plourde, B.L.T., Robertson, T.L., Wu, C.E., Ustinov, A.V., Clarke, J.: Solid-state qubits with current-controlled coupling. Science 314(5804), 1427 (2006)
Johnson, J.E., Hoskinson, E.M., Macklin, C., Slichter, D.H., Siddiqi, I., Clarke, J.: Dispersive readout of a flux qubit at the single-photon level. Phys. Rev. B 84, 220503 (2011)
Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)
Yan, F., Gustavsson, S., Kamal, A., Birenbaum, J., Sears, A.P., Hover, D., Gudmundsen, T.J., Rosenberg, D., Samach, G., Weber, S., Yoder, J.L., Orlando, T.P., Clarke, J., Kerman, A.J., Oliver, W.D.: The flux qubit revisited to enhance coherence and reproducibility. Nat. Commun. 7, 12964 (2016)
Leek, P.J., Baur, M., Fink, J.M., Bianchetti, R., Steffen, L., Filipp, S., Wallraff, A.: Cavity quantum electrodynamics with separate photon storage and qubit readout modes. Phys. Rev. Lett. 104, 100504 (2010)
Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623 (2013)
Megrant, A., et al.: Planar superconducting resonators with internal quality factors above one million. Appl. Phys. Lett. 100, 113510 (2012)
Hofheinz, M., Wang, H., Ansmann, M., Bialczak, R.C., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Wenner, J., Martinis, J.M., Cleland, A.N.: Synthesizing arbitrary quantum states in a superconducting resonator. Nature (London) 459, 546 (2009)
Houck, Andrew A., Treci, Hakan E., Koch, Jens: On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292 (2012)
Wulschner, F., Goetz, J., Koessel, F.R., Hoffmann, E., Baust, A., Eder, P., Fischer, M., Haeberlein, M., Schwarz, M.J., Pernpeintner, M.: Tunable coupling of transmission-line microwave resonators mediated by an rf squid. Epj Quantum Technology 3, 10 (2015)
Acknowledgements
The work was partly supported by the National Nature Science Foundation of China (Grant Nos. 11704306 and 11534008) and the National Key R&D Project (Grant No. 2016YFA0301404), and the China Postdoctoral Science Foundation (Grant No. 2016M602795).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Ma, S., Zhou, Y. et al. Generation and swapping of multi-qubit entangled state in a coupled superconducting resonator array. Quantum Inf Process 17, 336 (2018). https://doi.org/10.1007/s11128-018-2102-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-018-2102-8