Single-step multipartite entangled states generation from coupled circuit cavities

Abstract

Green–Horne–Zeilinger states are a typical type of multipartite entangled states, which plays a central role in quantum information processing. For the generation of multipartite entangled states, the singlestep method is more preferable as the needed time will not increase with the increasing of the qubit number. However, this scenario has a strict requirement that all two-qubit interaction strengths should be the same, or the generated state will be of low quality. Here, we propose a scheme for generating multipartite entangled states of superconducting qubits, from a coupled circuit cavities scenario, where we rigorously achieve the requirement via adding an extra z-direction ac classical field for each qubit, leading the individual qubit-cavity coupling strength to be tunable in a wide range, and thus can be tuned to the same value. Meanwhile, in order to obtain our wanted multi-qubits interaction, xdirection ac classical field for each qubit is also introduced. By selecting the appropriate parameters, we numerically shown that high-fidelity multi-qubit GHZ states can be generated. In addition, we also show that the coupled cavities scenario is better than a single cavity case. Therefore, our proposal represents a promising alternative for multipartite entangled states generation.

Keywords

quantum information processing / quantum entanglement / quantum state engineering

References

[1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, 2000

[2] R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86(22), 5188 (2001)

[3] M. Hillery, V. Bužek, and A. Berthiaume, Quantum secret sharing, Phys. Rev. A 59(3), 1829 (1999)

[4] S. Lloyd, Universal quantum simulators, Science 273(5278), 1073 (1996)

[5] A. J. Leggett, Realism and the physical world, Rep. Prog. Phys. 71(2), 022001 (2008)

[6] P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, Quantum information processing and communication, Eur. Phys. J. D 36(2), 203(2005)

[7] D. M. Greenberger, M. Horne, A. Shimony, and A. Zeilinger, Bells theorem without inequalities, Am. J. Phys. 58(12), 1131 (1990)

[8] M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, Generation of three-qubit entangled states using superconducting phase qubits, Nature 467(7315), 570 (2010)

[9] 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)

[10] R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature 508(7497), 500 (2014)

[11] S. L. Su, X. Q. Shao, H. F. Wang, and S. Zhang, Scheme for entanglement generation in an atom-cavity system via dissipation, Phys. Rev. A 90(5), 054302 (2014)

[12] S. L. Su, Q. Guo, H. F. Wang, and S. Zhang, Simplified scheme for entanglement preparation with Rydberg pumping via dissipation, Phys. Rev. A 92(2), 022328 (2015)

[13] H. Paik, A. Mezzacapo, M. Sandberg, D. T. McClure, B. Abdo, A. D. Córcoles, O. Dial, D. F. Bogorin, B. L. T. Plourde, M. Steffen, A. W. Cross, J. M. Gambetta, and J. M. Chow, Experimental demonstration of a resonatorinduced phase gate in a multiqubit circuit-QED system, Phys. Rev. Lett. 117(25), 250502 (2016)

[14] 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)

[15] L. Dong, Y. F. Lin, Q. Y. Li, H. K. Dong, X. M. Xiu, and Y. J. Gao, Generation of three-photon polarizationentangled decoherence-free states, Ann. Phys. 371, 287 (2016)

[16] M. X. Dong, W. Zhang, Z. B. Hou, Y. C. Yu, S. Shi, D. S. Ding, and B. S. Shi, Experimental realization of narrowband four-photon Greenberger–Horne–Zeilinger state in a single cold atomic ensemble, Opt. Lett. 42(22), 4691 (2017)

[17] X. Q. Shao, D. X. Li, Y. Q. Ji, J. H. Wu, and X. X. Yi, Groundstate blockade of Rydberg atoms and application in entanglement generation, Phys. Rev. A 96(1), 012328 (2017)

[18] R. Y. Yan, Z. B. Feng, C. L. Zhang, M. Li, X. J. Lu, and Y. Q. Zhou, Fast generations of entangled states between a transmon qubit and microwave photons via shortcuts to adiabaticity, Laser Phys. Lett. 15(11), 115205 (2018)

[19] 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)

[20] X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, Experimental ten-photon entanglement, Phys. Rev. Lett. 117(21), 210502 (2016)

[21] Z. Jin, S. L. Su, A. D. Zhu, H. F. Wang, and S. Zhang, Engineering multipartite steady entanglement of distant atoms via dissipation, Front. Phys. 13(5), 134209 (2018)

[22] K. Mølmer and A. Sørensen, Multiparticle entanglement of hot trapped ions, Phys. Rev. Lett. 82(9), 1835 (1999)

[23] S. B. Zheng, One-step synthesis of multiatom Greenberger-Horne-Zeilinger states, Phys. Rev. Lett. 87(23), 230404 (2001)

[24] F. Plastina, R. Fazio, and G. Massimo Palma, Macroscopic entanglement in Josephson nanocircuits, Phys. Rev. B 64(11), 113306 (2001)

[25] S. B. Zheng, Quantum-information processing and multiatom-entanglement engineering with a thermal cavity, Phys. Rev. A 66(6), 060303 (2002)

[26] D. I. Tsomoko, S. Ashhab, and F. Nori, Fully connected net-work of superconducting qubits in a cavity, New J. Phys. 10(11), 113020 (2008)

[27] A. Galiautdinov and J. M. Martinis, Maximally entangling tripartite protocols for Josephson phase qubits, Phys. Rev. A 78, 010305(R) (2008)

[28] J. Zhang, Y. X. Liu, C. W. Li, T. J. Tarn, and F. Nori, Generating stationary entangled states in superconducting qubits, Phys. Rev. A 79(5), 052308 (2009)

[29] C. L. Hutchison, J. M. Gambetta, A. Blais, and F. K. Wilhelm, Quantum trajectory equation for multiple qubits in circuit QED: Generating entanglement by measurement, Can. J. Phys. 87(3), 225 (2009)

[30] Y. D. Wang, S. Chesi, D. Loss, and C. Bruder, One-step multiqubit Greenberger–Horne–Zeilinger state generation in a circuit QED system, Phys. Rev. B 81(10), 104524 (2010)

[31] 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)

[32] T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hansel, M. Hennrich, and R. Blatt, 14-qubit entanglement: Creation and coherence, Phys. Rev. Lett. 106(13), 130506 (2011)

[33] Y. P. Zhong, D. Xu, P. Wang, C. Song, Q. J.Guo, W. X. Liu, K. Xu, B. X. Xia, C. Y. Lu, S. Han, J. W. Pan, and H. Wang, Emulating anyonic fractional statistical behavior in a superconducting quantum circuit, Phys. Rev. Lett. 117(11), 110501 (2016)

[34] 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)

[35] 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)

[36] J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011)

[37] M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339(6124), 1169 (2013)

[38] X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718-719, 1 (2017)

[39] E. Solano, G. S. Agarwal, and H. Walther, Strongdriving-assisted multipartite entanglement in cavity QED, Phys. Rev. Lett. 90(2), 027903 (2003)

RIGHTS & PERMISSIONS

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