Abstract
Circuit quantum electrodynamics system composed of many qubits and resonators may provide an excellent way to realize large-scale quantum information processing (QIP). Because of key role for large-scale QIP and quantum computation, multi-qubit gates have drawn intensive attention recently. Here, we present a one-step method to achieve a multi-target-qubit controlled phase gate in a multi-resonator system, which possesses a common control qubit and multiple different target qubits distributed in their respective resonators. Noteworthily, the implementation of this multi-qubit phase gate does not require classical pulses, and the gate operation time is independent of the number of qubits. Besides, the proposed scheme can in principle be adapted to a general type of qubits like natural atoms, quantum dots, and solid-state qubits (e.g., superconducting qubits and NV centers).





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Clarke, J., Wilhelm, F.K.: Superconducting quantum bits. Nature 453, 1031–1042 (2008)
You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature 474, 589–597 (2011)
Buluta, I., Ashhab, S., Nori, F.: Natural and artificial atoms for quantum computation. Rep. Prog. Phys. 74, 104401 (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)
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)
Koch, J., Yu, T.M., Gambetta, J., Houck, A.A., Schuster, D.I., Majer, J., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)
Chow, J.M., Gambetta, J.M., Córcoles, A.D., Merkel, S.T., Smolin, J.A., Rigetti, C., Poletto, S., Keefe, G.A., Rothwell, M.B., Rozen, J.R., Ketchen, M.B., Steffen, M.: Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits. Phys. Rev. Lett. 109, 060501 (2012)
Chang, J.B., Vissers, M.R., Corcoles, A.D., Sandberg, M., Gao, J., Abraham, D.W., Chow, J.M., Gambetta, J.M., Rothwell, M.B., Keefe, G.A., Steffen, M., Pappas, D.P.: Improved superconducting qubit coherence using titanium nitride. Appl. Phys. Lett. 103, 012602 (2013)
Barends, R., Kelly, J., Megrant, A., Sank, D., Jeffrey, E., Chen, Y., Yin, Y., Chiaro, B., Mutus, J.Y., Neill, C., O’Malley, P.J.J., Roushan, P., Wenner, J., White, T.C., Cleland, A.N., Martinis, J.M.: Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013)
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. Nature Commun. 5, 4015 (2014)
Chen, Y., Neill, C., Roushan, P., Leung, N., Fang, M., Barends, R., Kelly, J., Campbell, B., Chen, Z., Chiaro, B., Dunsworth, A., Jeffrey, E., Megrant, A., Mutus, J.Y., O’Malley, P.J.J., Quintana, C.M., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Geller, M.R., Cleland, A.N., Martinis, J.M.: Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014)
Stern, M., Catelani, G., Kubo, Y., Grezes, C., Bienfait, A., Vion, D., Esteve, D., Bertet, P.: Flux qubits with long coherence times for hybrid quantum circuits. Phys. Rev. Lett. 113, 123601 (2014)
Peterer, M.J., Bader, S.J., Jin, X., Yan, F., Kamal, A., Gudmundsen, T.J., Leek, P.J., Orlando, T.P., Oliver, W.D., Gustavsson, S.: Coherence and decay of higher energy levels of a superconducting transmon qubit. Phys. Rev. Lett. 114, 010501 (2015)
Pop, I.M., Geerlings, K., Catelani, G., Schoelkopf, R.J., Glazman, L.I., Devore, M.H.: Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014)
You, J.Q., Hu, X.D., Ashhab, S., Nori, F.: Low-decoherence flux qubit. Phys. Rev. B 75, 140515 (2007)
Steffen, M., Kumar, S., DiVincenzo, D.P., Rozen, J.R., Keefe, G.A., Rothwell, M.B., Ketchen, M.B.: High-coherence hybrid superconducting qubit. Phys. Rev. Lett. 105, 100502 (2010)
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. Nature Commun. 7, 12964 (2016)
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 431, 162–167 (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 431, 159–162 (2004)
Forn-Díaz, P., Lisenfeld, J., Marcos, D., Garc ía-Ripoll, J.J., Solano, E., Harmans, C.J.P.M., Mooij, J.E.: Observation of the Bloch–Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime. Phys. Rev. Lett. 105, 237001 (2010)
Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., Garcia-Ripoll, J.J., Zueco, D., Hümmer, T., Solano, E., Marx, A., Gross, R.: Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nat. Phys. 6, 772–776 (2010)
Baust, A., Hoffmann, E., Haeberlein, M., Schwarz, M.J., Eder, P., Goetz, J., Wulschner, F., Xie, E., Zhong, L., Quijandŕa, F., Zueco, D., García Ripoll, J.J., García-Alvarez, L., Romero, G., Solano, E., Fedorov, K.G., Menzel, E.P., Deppe, F., Marx, A., Gross, R.: Ultrastrong coupling in two-resonator circuit QED. Phys. Rev. B 93, 214501 (2016)
Yoshihara, F., Fuse, T., Ashhab, S., Kakuyanagi, K., Saito, S., Semba, K.: Superconducting qubitoscillator circuit beyond the ultrastrong-coupling regime. Nat. Phys. 13, 44–47 (2017)
Mariantoni, M., Deppe, F., Marx, A., Gross, R., Wilhelm, F.K., Solano, E.: Two-resonator circuit quantum electrodynamics: a superconducting quantum switch. Phys. Rev. B 78, 104508 (2008)
Strauch, F.W., Jacobs, K., Simmonds, R.W.: Arbitrary control of entanglement between two superconducting resonators. Phys. Rev. Lett. 105, 050501 (2010)
Merkel, S.T., Wilhelm, F.K.: Generation and detection of NOON states in superconducting circuits. New J. Phys. 12, 093036 (2010)
Hu, Y., Tian, L.: Deterministic generation of entangled photons in superconducting resonator arrays. Phys. Rev. Lett. 106, 257002 (2011)
Strauch, F.W.: Quantum logic gates for superconducting resonator qudits. Phys. Rev. A 84, 052313 (2011)
Strauch, F.W., Onyango, D., Jacobs, K., Simmonds, R.W.: Entangled-state synthesis for superconducting resonators. Phys. Rev. A 85, 022335 (2012)
Peng, Z.H., Liu, Y.X., Nakamura, Y., Tsai, J.S.: Fast generation of multiparticle entangled state for flux qubits in a circle array of transmission line resonators with tunable coupling. Phys. Rev. B 85, 024537 (2012)
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)
Aron, C., Kulkarni, M., Türeci, H.E.: Steady-state entanglement of spatially separated qubits via quantum bath engineering. Phys. Rev. A 90, 062305 (2014)
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)
Sharma, R., Strauch, F.W.: Quantum state synthesis of superconducting resonators. Phys. Rev. A 93, 012342 (2016)
Kyriienko, O., Søensen, A.S.: Continuous-wave single-photon transistor based on a superconducting circuit. Phys. Rev. Lett. 117, 140503 (2016)
Zhao, Y.J., Wang, C.Q., Zhu, X.B., Liu, Y.X.: Engineering entangled microwave photon states through multiphoton interactions between two cavity fields and a superconducting qubit. Sci. Rep. 6, 23646 (2016)
Li, Z., Ma, S.L., Yang, Z.P., Fang, A.P., Li, P.B., Gao, S.Y., Li, F.L.: Generation and replication of continuous-variable quadripartite cluster and Greenberger–Horne–Zeilinger states in four chains of superconducting transmission line resonators. Phys. Rev. A 93, 042305 (2016)
Yang, C.P., Su, Q.P., Zheng, S.B., Nori, F.: Entangling superconducting qubits in a multi-cavity system. New J. Phys. 18, 013025 (2016)
Li, W.L., Li, C., Song, H.S.: Realization of quantum information processing in quantum star network constituted by superconducting hybrid systems. Phys. A 463, 427–436 (2016)
Su, Q.P., Zhu, H.H., Yu, L., Zhang, Y., Xiong, S.J., Liu, J.M., Yang, C.P.: Generating double NOON states of photons in circuit QED. Phys. Rev. A 95, 022339 (2017)
Liu, T., Zhang, Y., Yu, C.S., Zhang, W.N.: Deterministic transfer of an unknown qutrit state assisted by the low-Q microwave resonators. Phys. Lett. A 381, 1727–1731 (2017)
Mariantoni, M., Wang, H., Yamamoto, T., Neeley, M., Bialczak, R.C., Chen, Y., Lenander, M., Lucero, E., O’connell, A.D., Sank, D., Weides, M., Wenner, J., Yin, Y., Zhao, J., Korotkov, A.N., Cleland, A.N., Martinis, J.M.: Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011)
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)
Steffen, L., Salathe, Y., Oppliger, M., Kurpiers, P., Baur, M., Lang, C., Eichler, C., Puebla-Hellmann, G., Fedorov, A., Wallraff, A.: Deterministic quantum teleportation with feed-forward in a solid state system. Nature 500, 319–322 (2013)
Wang, C., Gao, Y.Y., Reinhold, P., Heeres, R.W., Ofek, N., Chou, K., Axline, C., Reagor, M., Blumoff, J., Sliwa, K.M., Frunzio, L., Girvin, S.M., Jiang, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: A Schrdinger cat living in two boxes. Science 352, 1087–1091 (2016)
Ofek, N., Petrenko, A., Heeres, R., Reinhold, P., Leghtas, Z., Vlastakis, B., Liu, Y., Frunzio, L., Girvin, S.M., Jiang, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016)
Kakuyanagi, K., Matsuzaki, Y., Déprez, C., Toida, H., Semba, K., Yamaguchi, H., Munro, W.J., Saito, S.: Observation of collective coupling between an engineered ensemble of macroscopic artificial atoms and a superconducting resonator. Phys. Rev. Lett. 117, 210503 (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)
Wang, X., Sørensen, A., Mølmeret, K.: Multibit gates for quantum computing. Phys. Rev. Lett. 86, 3907 (2001)
Duan, L.M., Wang, B., Kimble, H.J.: Robust quantum gates on neutral atoms with cavity-assisted photon scattering. Phys. Rev. A 72, 032333 (2005)
Zou, X., Dong, Y., Guo, G.C.: Implementing a conditional \(z\) gate by a combination of resonant interaction and quantum interference. Phys. Rev. A 74, 032325 (2006)
Xiao, Y.F., Zou, X.B., Guo, G.C.: One-step implementation of an \(N\)-qubit controlled-phase gate with neutral atoms trapped in an optical cavity. Phys. Rev. A 75, 054303 (2007)
Monz, T., Kim, K., Hänsel, 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)
Jones, C.: Composite Toffoli gate with two-round error detection. Phys. Rev. A 87, 052334 (2013)
Wei, H.R., Deng, F.G.: Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities. Phys. Rev. A 87, 022305 (2013)
Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling \(n\) qubits in a cavity. Phys. Rev. A 81, 062323 (2010)
Yang, C.P., Su, Q.P., Zhang, F.Y., Zheng, S.B.: Single-step implementation of a multiple-target-qubit controlled phase gate without need of classical pulses. Opt. Lett. 39, 3312–3315 (2014)
Wang, H.F., Zhu, A.D., Zhang, S.: One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities. Opt. Lett. 39, 1489–1492 (2014)
Liu, T., Cao, X.Z., Su, Q.P., Xiong, S.J., Yang, C.-P.: Multi-target-qubit unconventional geometric phase gate in a multi-cavity system. Sci. Rep. 6, 21562 (2016)
Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)
Möttönen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93, 130502 (2004)
Shor, P.W.: In: Goldwasser S. (ed.) Proceedings of the 35th annual symposium on foundations of computer science, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)
Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80, 4329 (1998)
Nilsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995)
Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793 (1996)
Gaitan, F.: Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, Boca Raton (2008)
Beth, T., Rötteler, M.: Quantum Information, vol. 173, Ch. 4, p. 96. Springer, Berlin (2001)
Šašura, M., Bužek, V.: Multiparticle entanglement with quantum logic networks: application to cold trapped ions. Phys. Rev. A 64, 012305 (2001)
Braunstein, S.L., Bužek, V., Hillery, M.: Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit. Phys. Rev. A 63, 052313 (2001)
Liu, Y.X., Sun, C.P., Nori, F.: Scalable superconducting qubit circuits using dressed states. Phys. Rev. A 74, 052321 (2006)
Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Katz, N., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M.: Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4, 523–526 (2008)
Leek, P.J., Filipp, S., Maurer, P., Baur, M., Bianchetti, R., Fink, J.M., Göppl, M., Steffen, L., Wallraff, A.: Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79, 180511 (2009)
Strand, J.D., Ware, M., Beaudoin, F., Ohki, T.A., Johnson, B.R., Blais, A., Plourde, B.L.T.: First-order sideband transitions with flux-driven asymmetric transmon qubits. Phys. Rev. B 87, 220505 (2013)
Liu, Y.X., You, J.Q., Wei, L.F., Sun, C.P., Nori, F.: Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit. Phys. Rev. Lett. 95, 087001 (2005)
James, D.F., Jerke, J.: Effective Hamiltonian theory and its applications in quantum information. Can. J. Phys. 85, 625–632 (2007)
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)
Wang, Z.L., Zhong, Y.P., He, L.J., Wang, H., Martinis, J.M., Cleland, A.N., Xie, Q.W.: Quantum state characterization of a fast tunable superconducting resonator. Appl. Phys. Lett. 102, 163503 (2013)
Chen, W., Bennett, D.A., Patel, V., Lukens, J.E.: Substrate and process dependent losses in superconducting thin film resonators. Supercond. Sci. Technol. 21, 075013 (2008)
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)
Megrant, A., Neill, C., Barends, R., Chiaro, B., Chen, Y., Feigl, L., Kelly, J., Lucero, E., Mariantoni, M., O’Malley, P.J.J., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Yin, Y., Zhao, J., Palmstrøm, C.J., Martinis, J.M., Cleland, A.N.: Planar superconducting resonators with internal quality factors above one million. Appl. Phys. Lett. 100, 113510 (2012)
Acknowledgements
This work was supported by the National Natural Science Foundation of China, under Grant Nos. 11775040 and 11375036, the Xinghai Scholar Cultivation Plan, and the Fundamental Research Fund for the Central Universities under Grant No. DUT18LK45.
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Liu, T., Guo, BQ., Zhang, Y. et al. One-step implementation of a multi-target-qubit controlled phase gate in a multi-resonator circuit QED system. Quantum Inf Process 17, 240 (2018). https://doi.org/10.1007/s11128-018-2011-x
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DOI: https://doi.org/10.1007/s11128-018-2011-x