Abstract
An efficient scheme is proposed for generating n-qubit Greenberger–Horne–Zeilinger states of n superconducting qubits separated by (\(n-1\)) coplanar waveguide resonators capacitively via adiabatic passage with the help of quantum Zeno dynamics in one step. In the scheme, it is not necessary to precisely control the time of the whole operation and the Rabi frequencies of classical fields because of the introduction of adiabatic passage. The numerical simulations for three-qubit Greenberger–Horne–Zeilinger state show that the scheme is insensitive to the dissipation of the resonators and the energy relaxation of the superconducting qubits. The three-qubit Greenberger–Horne–Zeilinger state can be deterministically generated with comparatively high fidelity in the current experimental conditions, though the scheme is somewhat sensitive to the dephasing of superconducting qubits.






Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392–2395 (2000)
Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003)
Zheng, S.B.: One-step synthesis of multiatom Greenberger–Horne–Zeilinger states. Phys. Rev. Lett. 87, 230404 (2001)
Chen, Y.H., Xia, Y., Song, J., Chen, Q.Q.: Shortcuts to adiabatic passage for fast generation of Greenberger–Horne–Zeilinger states by transitionless quantum driving. Sci. Rep. 5, 15616 (2015)
Feng, W., Wang, P., Ding, X., Xu, L., Li, X.Q.: Generating and stabilizing the Greenberger–Horne–Zeilinger state in circuit QED: joint measurement, Zeno effect, and feedback. Phys. Rev. A 83, 042313 (2011)
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)
Duan, L.M., Kimble, H.J.: Efficient engineering of multiatom entanglement through single-photon detections. Phys. Rev. Lett. 90, 253601 (2003)
Huang, Y.F., Liu, B.H., Peng, L., Li, Y.H., Li, L., Li, C.F., Guo, G.C.: Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state. Nat. Commun. 2, 546 (2011)
Monz, T., Schindler, P., Barreiro, J.T., Chwalla, M., Nigg, D., Coish, W.A., Harlander, M., Hänsel, W., Hennrich, M., Blatt, R.: 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011)
Chow, J.M., Gambetta, J.M., Magesan, E., Abraham, D.W., Cross, A.W., Johnson, B.R., Masluk, N.A., Ryan, C.A., Smolin, J.A., Srinivasan, S.J., Steffen, M.: Implementing a strand of a scalable fault-tolerant quantum computing fabric. Nat. Commun. 5, 4015 (2014)
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)
Dogra, S., Dorai, K., Arvind.: Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor. Phys. Rev. A 91, 022312 (2015)
Makhlin, Y., Schön, G., Shnirman, A.: Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001)
Pashkin, Y.A., Yamamoto, T., Astafiev, O., Nakamura, Y., Averin, D.V., Tsai, J.S.: Quantum oscillations in two coupled charge qubits. Nature (London) 421, 823–826 (2003)
Yu, Y., Han, S., Chu, X., Chu, S.I., Wang, Z.: Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science 296, 889–892 (2002)
Vion, D., Aassime, A., Cottet, A., Joyez, P., Pothier, H., Urbina, C., Esteve, D., Devoret, M.H.: Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)
Liu, Y.X., Wei, L.F., Nori, F.: Generation of nonclassical photon states using a superconducting qubit in a microcavity. Europhys. Lett. 67, 941–947 (2004)
Song, K.H., Zhou, Z.W., Guo, G.C.: Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition. Phys. Rev. A 71, 052310 (2005)
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)
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)
Liu, Q.G., Wu, Q.C., Leng, C.L., Liang, Y., Ji, X., Zhang, S.: Generation of atomic NOON states via adiabatic passage. Quantum Inf. Process. 13, 2801–2814 (2014)
Wei, X., Chen, M.F.: Preparation of multi-qubit W states in multiple resonators coupled by a superconducting qubit via adiabatic passage. Quantum Inf. Process. 14, 2419–2433 (2015)
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, 546–549 (2009)
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)
Bergmann, K., Theuer, H., Shore, B.W.: Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003–1025 (1998)
Král, P., Thanopulos, I., Shapiro, M.: Colloquium: coherently controlled adiabatic passage. Rev. Mod. Phys. 79, 53–77 (2007)
Hao, S.Y., Xia, Y., Song, J., An, N.B.: One-step generation of multiatom Greenberger–Horne–Zeilinger states in separate cavities via adiabatic passage. J. Opt. Soc. Am. B 30, 468–474 (2013)
Shao, X.Q., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Deterministic generation of arbitrary multiatom symmetric Dicke states by a combination of quantum Zeno dynamics and adiabatic passage. Europhys. Lett. 90, 50003 (2010)
Shi, Z.C., Xia, Y., Song, J., Song, H.S.: Generation of three-atom singlet state in a bimodal cavity via quantum Zeno dynamics. Quantum Inf. Process. 12, 411–424 (2013)
Wu, Q.C., Wang, Y., Ji, X.: Preparation of three-qubit decoherence-free state via quantum Zeno dynamics. Quantum Inf. Process. 12, 2121–2130 (2013)
Chen, Y.H., Xia, Y., Song, J.: Deterministic generation of singlet states for N-atoms in coupled cavities via quantum Zeno dynamics. Quantum Inf. Process. 13, 1857–1877 (2014)
Liang, Y., Su, S.L., Wu, Q.C., Ji, X., Zhang, S.: Adiabatic passage for three-dimensional entanglement generation through quantum Zeno dynamics. Opt. Express 23, 5064–5077 (2015)
Chen, M.F., Chen, Y.F., Ma, S.S.: One-step implementation of a Toffoli gate of separated superconducting qubits via quantum Zeno dynamics. Quantum Inf. Process. 15, 1469–1483 (2016)
Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)
Facchi, P., Marmo, G., Pascazio, S.: Quantum Zeno dynamics and quantum Zeno subspaces. J. Phys. Conf. Ser. 196, 012017 (2009)
Vitanov, N.V., Suominen, K.A., Shore, B.W.: Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage. J. Phys. B 32, 4535–4546 (1999)
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)
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)
Feng, Z.B., Zhang, X.D.: Holonomic quantum computation with superconducting charge-phase qubits in a cavity. Phys. Lett. A 372, 1589–1594 (2008)
Zahedinejad, E., Ghosh, J., Sanders, B.C.: High-fidelity single-shot Toffoli gate via quantum control. Phys. Rev. Lett. 114, 200502 (2015)
Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623–653 (2013)
Paik, H., Schuster, D.I., Bishop, L.S., Kirchmair, G., Catelani, G., Sears, A.P., Johnson, B.R., Reagor, M.J., Frunzio, L., Glazman, L.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011)
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. Rev. B 86, 100506 (2012)
Makhlin, Y., Shnirman, A.: Dephasing of solid-state qubits at optimal points. Phys. Rev. Lett. 92, 178301 (2004)
Cywiński, Ł., Lutchyn, R.M., Nave, C.P., Sarma, S.D.: How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008)
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant Nos. 11464046 and 61465013.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, JL., Song, C., Xu, J. et al. Adiabatic passage for one-step generation of n-qubit Greenberger–Horne–Zeilinger states of superconducting qubits via quantum Zeno dynamics. Quantum Inf Process 15, 3663–3675 (2016). https://doi.org/10.1007/s11128-016-1366-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-016-1366-0