Abstract
We propose a protocol to implement controlled-not (C-NOT) gates of two superconducting quantum interference device (SQUID) qubits in a cavity. The Rabi frequencies of driven pulses are designed by means of the shortcuts to adiabaticity. The numerical simulations show that the fidelities of the C-NOT gates are insensitive to the deviations of control parameters. Besides, the C-NOT gates are robust against the decoherent factors, such as spontaneous emissions and dephasings of the SQUID qubits and the decay of the cavity mode. Therefore, the protocol may be useful in the fields of quantum computations.
Similar content being viewed by others
References
Lloyd, S.: Ultimate physical limits to computation. Nature 406, 1047 (2000)
Ng, Y.J.: From computation to black holes and space-time foam. Phys. Rev. Lett. 86, 2946 (2001)
Wang, X.G., Sørensen, A., Mølmer, K.: Multibit gates for quantum computing. Phys. Rev. Lett. 86, 3907 (2001)
Ozawa, M.: Conservative quantum computing. Phys. Rev. Lett. 89, 057902 (2002)
Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, vol. 124. IEEE Computer Society Press, Los Alamitos (1994)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484 (1997)
Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80, 4329 (1998)
Deng, Z.J., Zhang, X.L., Wei, H., Gao, K.L., Feng, M.: Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference. Phys. Rev. A 76, 044305 (2007)
Bonato, C., Haupt, F., Oemrawsingh, S.S.R., Gudat, J., Ding, D., van Exter, M.P., Bouwmeester, D.: CNOT and Bell-state analysis in the weak-coupling cavity QED regime. Phys. Rev. Lett. 104, 160503 (2010)
Duan, L.M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interaction. Phys. Rev. Lett. 92, 127902 (2004)
Ren, B.C., Deng, F.G.: Hyper-parallel photonic quantum computation with coupled quantum dots. Sci. Rep. 4, 4623 (2014)
Ren, B.C., Wei, H.R., Deng, F.G.: Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity. Laser Phys. Lett. 10, 2241 (2013)
Liu, B.J., Huang, Z.H., Xue, Z.Y., Zhang, X.D.: Superadiabatic holonomic quantum computation in cavity QED. Phys. Rev. A 95, 062308 (2017)
Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states. Phys. Rev. A 91, 012325 (2015)
Shao, X.Q., Li, D.X., Ji, Y.Q., Wu, J.H., Yi, X.X.: Ground-state blockade of Rydberg atoms and application to multipartite entanglement. Phys. Rev. A 96, 012328 (2017)
Liang, Z.T., Yue, X., Lv, Q., Du, Y.X., Huang, W., Yan, H., Zhu, S.L.: Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers. Phys. Rev. A 93, 040305(R) (2016)
Du, Y.X., Liu, B.J., Lv, Q.X., Zhang, X.D., Yan, H., Zhu, S.L.: Degenerate eigensubspace in a triangle-level system and its geometric quantum control. Phys. Rev. A 96, 012333 (2017)
DiVincenzo, D.P.: Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015 (1995)
Sleator, T., Weinfurter, H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087 (1995)
Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)
Shao, X.Q., Chen, L., Zhang, S., Yeon, K.H.: Distributed CNOT gate via quantum Zeno dynamics. J. Phys. B 42, 165507 (2009)
Wu, J.L., Ji, X., Zhang, S.: Dressed-state scheme for a fast CNOT gate. Quantum Inf. Process. 16, 294 (2017)
Galiautdinov, A.: Generation of high-fidelity controlled-not logic gates by coupled superconducting qubits. Phys. Rev. A 75, 052303 (2007)
Rigetti, C., Devoret, M.: Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies. Phys. Rev. B 81, 134507 (2010)
Rigetti, C., Blais, A., Devoret, M.: Controlled-NOT logic with nonresonant Josephson phase qubits. Phys. Rev. Lett. 94, 240502 (2005)
Chow, J.M., Córcoles, A.D., Gambetta, J.M., Rigetti, C., Johnson, B.R., Smolin, J.A., Rozen, J.R., Keefe, G.A., Rothwell, M.B., Ketchen, M.B., Steffen, M.: Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits. Phys. Rev. Lett. 109, 060501 (2012)
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)
Goto, H., Ichimura, K.: Multiqubit controlled unitary gate by adiabatic passage with an optical cavity. Phys. Rev. A 70, 012305 (2004)
Chow, J.M., Gambetta, J.M., Cross, A.W., Merkel, S.T., Rigetti, C., Steffen, M.: Microwave-activated conditional-phase gate for superconducting qubits. New J. Phys. 15, 115012 (2013)
Iakoupov, I., Borregaard, J., Sørensen, A.S.: Controlled-phase gate for photons based on stationary light. Phys. Rev. Lett. 120, 010502 (2018)
Liang, Y., Wu, Q.C., Su, S.L., Ji, X., Zhang, S.: Shortcuts to adiabatic passage for multiqubit controlled phase gate. Phys. Rev. A 91, 032304 (2015)
Xue, Z.Y., Zhang, G., Dong, P., Yi, Y.M., Cao, Z.L.: Quantum controlled phase gate and cluster states generation via two superconducting quantum interference devices in a cavity. Eur. Phys. J. B 52, 333 (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., 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)
Song, K.H., Zhao, Y.J., Shi, Z.G., Xiang, S.H., Chen, X.W.: Simultaneous implementation of n SWAP gates using superconducting charge qubits coupled to a cavity. Opt. Commun. 283, 506 (2010)
Wu, T., Ye, L.: Implementing two-qubit SWAP gate with SQUID qubits in a microwave cavity via adiabatic passage evolution. Int. J. Theor. Phys. 51, 1076 (2012)
Zhang, F.Y., Pei, P., Wang, Z., Song, H.S.: Realizing a SWAP gate and generating cluster states in a controllable superconducting coupling system. Phys. Scr. 82, 065010 (2010)
Sangouard, N., Lacour, X., Guérin, S., Jauslin, H.R.: Fast SWAP gate by adiabatic passage. Phys. Rev. A 72, 062309 (2005)
Liang, L., Li, C.: Realization of quantum SWAP gate between flying and stationary qubits. Phys. Rev. A 72, 024303 (2005)
Duan, L.M., Kuzmich, A., Kimble, H.J.: Cavity QED and quantum-information processing with “hot” trapped atoms. Phys. Rev. A 67, 032305 (2003)
van den Brink, A.M.: Hamiltonian for coupled flux qubits. Phys. Rev. B 71, 064503 (2005)
You, J.Q., Hu, X., Ashhab, S., Nori, F.: Low-decoherence flux qubit. Phys. Rev. B 75, 140515(R) (2007)
Kakuyanagi, K., Meno, T., Saito, S., Nakano, H., Semba, K., Takayanagi, H., Deppe, F., Shnirman, A.: Dephasing of a superconducting flux qubit. Phys. Rev. Lett. 98, 047004 (2007)
Saito, S., Meno, T., Ueda, M., Tanaka, H., Semba, K., Takayanagi, H.: Parametric control of a superconducting flux qubit. Phys. Rev. Lett. 96, 107001 (2006)
Duty, T., Gunnarsson, D., Bladh, K., Delsing, P.: Coherent dynamics of a Josephson charge qubit. Phys. Rev. B 69, 140503(R) (2004)
Astafiev, O., Pashkin, Y.A., Nakamura, Y., Yamamoto, T., Tsai, J.S.: Quantum noise in the Josephson charge qubit. Phys. Rev. Lett. 93, 267007 (2004)
Ralph, J.F., Griffith, E.J., Clark, T.D., Everitt, M.J.: Guidance and control in a Josephson charge qubit. Phys. Rev. B 70, 214521 (2004)
Li, J., Johansson, G.: Simultaneous readout of two charge qubits. Phys. Rev. B 75, 085312 (2007)
Amin, M.H.S., Smirnov, A.Y., van den Brink, A.M.: Josephson-phase qubit without tunneling. Phys. Rev. B 67, 100508(R) (2003)
Kosugi, N., Matsuo, S., Fujii, T., Hatakenaka, N.: Josephson phase qubit with an optimal point. Phys. Rev. B 81, 024507 (2010)
Steffen, M., Martinis, J.M., Chuang, I.L.: Accurate control of Josephson phase qubits. Phys. Rev. B 68, 224518 (2003)
Galiautdinov, A.: Controlled-NOT logic with nonresonant Josephson phase qubits. Phys. Rev. A 79, 042316 (2009)
Schutjens, R., Dagga, F.A., Egger, D.J., Wilhelm, F.K.: Single qubit gates in frequency-crowded transmon systems. Phys. Rev. A 88, 052330 (2013)
Lu, X.J., Li, M., Zhao, Z.Y., Zhang, C.L., Han, H.P., Feng, Z.B., Zhou, Y.Q.: Nonleaky and accelerated population transfer in a transmon qutrit. Phys. Rev. A 96, 023843 (2017)
Houck, A.A., Schreier, J.A., Johnson, B.R., Chow, J.M., Koch, J., Gambetta, J.M., Schuster, D.I., Frunzio, L., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Controlling the spontaneous emission of a superconducting transmon qubit. Phys. Rev. Lett. 101, 080502 (2008)
Feng, Z.B., Lu, X.J., Li, M., Yan, R.Y., Zhou, Y.Q.: Speeding up adiabatic population transfer in a Josephson qutrit via counter-diabatic driving. New J. Phys. 19, 123023 (2017)
Viola, G., Catelani, G.: Collective modes in the fluxonium qubit. Phys. Rev. B 92, 224511 (2015)
Herrera-Martí, D.A., Nazir, A., Barrett, S.D.: Tradeoff between leakage and dephasing errors in the fluxonium qubit. Phys. Rev. B 88, 094512 (2013)
Zhu, G., Ferguson, D.G., Manucharyan, V.E., Koch, J.: Circuit QED with fluxonium qubits: theory of the dispersive regime. Phys. Rev. B 87, 024510 (2013)
Meier, H., Brierley, R.T., Kou, A., Girvin, S.M., Glazman, L.I.: Signatures of quantum phase transitions in the dynamic response of fluxonium qubit chains. Phys. Rev. B 92, 064516 (2015)
Deng, Z.J., Gao, K.L., Feng, M.: Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage. Phys. Rev. A 74, 064303 (2006)
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)
Kis, Z., Paspalakis, E.: Arbitrary rotation and entanglement of flux SQUID qubits. Phys. Rev. B 69, 024510 (2004)
Genov, G.T., Vitanov, N.V.: Dynamical suppression of unwanted transitions in multistate quantumsystems. Phys. Rev. Lett. 110, 133002 (2013)
Torosov, B.T., Vitanov, N.V.: Smooth composite pulses for high-fidelity quantum information processing. Phys. Rev. A 83, 053420 (2011)
Zheng, S.B.: Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation. Reply Phys. Rev. Lett. 95, 080502 (2005)
Král, P., Thanopulos, I., Shapiro, M.: Colloquium: coherently controlled adiabatic passage. Rev. Mod. Phys. 79, 53 (2007)
Bergmann, K., Theuer, H., Shore, B.W.: Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003 (1998)
Fewell, M.P., Shore, B.W., Bergmann, K.: Coherent population transfer among three states: full algebraic solutions and the relevance of non adiabatic processes to transfer by delayed pulses. Aust. J. Phys. 50, 281 (1997)
Vitanov, N.V., Halfmann, T., Shore, B.W., Bergmann, K.: Laser-induced population transfer by adiabatic passage thchniques. Annu. Rev. Phys. Chem. 52, 763 (2001)
Daems, D., Ruschhaupt, A., Sugny, D., Guérin, S.: Robust quantum control by a single-shot shaped pulse. Phys. Rev. Lett. 111, 050404 (2013)
Sugny, D., Kontz, C.: Optimal control of a three-level quantum system by laser fields plus von Neumann measurements. Phys. Rev. A 77, 063420 (2008)
Van Damme, L., Schraft, D., Genov, G., Sugny, D., Halfmann, T., Guérin, S.: Robust not gate by single-shot-shaped pulses: demonstration of the efficiency of the pulses in rephasing atomic coherences. Phys. Rev. A 96, 022309 (2017)
Peirce, A.P., Dahleh, M.A., Rabitz, H.: Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950 (1988)
Lu, M., Xia, Y., Song, J., Song, H.S.: Driving three atoms into a singlet state in an optical cavity via adiabatic passage of a dark state. J. Phys. B 46, 015502 (2013)
Berry, M.V.: Transitionless quantum driving. J. Phys. A 42, 365303 (2009)
Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett. 105, 123003 (2010)
del Campo, A.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)
Chen, Y.H., Wu, Q.C., Huang, B.H., Song, J., Xia, Y.: Arbitrary quantum state engineering in three-state systems via counterdiabatic driving. Sci. Rep. 6, 38484 (2016)
Chen, X., Torrontegui, E., Muga, J.G.: Lewis–Riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)
del Campo, A., Rams, M.M., Zurek, W.H.: Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model. Phys. Rev. Lett. 109, 115703 (2012)
Chen, X., Ruschhaupt, A., Schmidt, S., del Campo, A., Guéry-Odelin, D., Muga, J.G.: Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. Phys. Rev. Lett. 104, 063002 (2010)
Torrontegui, E., Ibáñez, S., Martínez-Garaot, S., Modugno, M., del Campo, A., Guéry-Odelin, D., Ruschhaupt, A., Chen, X., Muga, J.G.: Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117 (2013)
Muga, J.G., Chen, X., Ruschhaupt, A., Guéry-Odelin, D.: Frictionless dynamics of Bose–Einstein condensates under fast trap variations. J. Phys. B 42, 241001 (2009)
del Campo, A., Boshier, M.G.: Shortcuts to adiabaticity in a time-dependent box. Sci. Rep. 2, 648 (2012)
Martínez-Garaot, S., Torrontegui, E., Chen, X., Muga, J.G.: Shortcuts to adiabaticity in three-level systems using Lie transforms. Phys. Rev. A 89, 053408 (2014)
Torrontegui, E., Martínez-Garaot, S., Muga, J.G.: Hamiltonian engineering via invariants and dynamical algebra. Phys. Rev. A 89, 043408 (2014)
Saberi, H., Opatrný, T., Mølmer, K., del Campo, A.: Adiabatic tracking of quantum many-body dynamics. Phys. Rev. A 90, 060301(R) (2014)
Torosov, B.T., DellaValle, G., Longhi, S.: Non-Hermitian shortcut to adiabaticity. Phys. Rev. A 87, 052502 (2013)
Torosov, B.T., DellaValle, G., Longhi, S.: Non-Hermitian shortcut to stimulated Raman adiabatic passage. Phys. Rev. A 89, 063412 (2014)
Ibáñez, S., Chen, X., Torrontegui, E., Muga, J.G., Ruschhaupt, A.: Multiple schrodinger pictures and dynamics in shortcuts to adiabaticity. Phys. Rev. Lett. 109, 100403 (2012)
Ibáñez, S., Chen, X., Muga, J.G.: Improving shortcuts to adiabaticity by iterative interaction pictures. Phys. Rev. A 87, 043402 (2013)
Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level superadiabatic quantum driving with multiple Schrödinger dynamics. Phys. Rev. A 93, 052324 (2016)
Baksic, A., Ribeiro, H., Clerk, A.A.: Speeding up adiabatic quantum state transfer by using dressed states. Phys. Rev. Lett. 116, 230503 (2016)
Torrontegui, E., Ibáñez, S., Chen, X., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Fast atomic transport without vibrational heating. Phys. Rev. A 83, 013415 (2011)
Muga, J.G., Chen, X., Ibáñez, S., Lizuain, I., Ruschhaupt, A.: Transitionless quantum drivings for the harmonic oscillator. J. Phys. B 43, 085509 (2010)
Torrontegui, E., Chen, X., Modugno, M., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Fast transitionless expansions of cold atoms in optical Gaussian beam traps. Phys. Rev. A 85, 033605 (2012)
Masuda, S., Nakamura, K.: Acceleration of adiabatic quantum dynamics in electromagnetic fields. Phys. Rev. A 84, 043434 (2011)
Masuda, S., Rice, S.A.: Fast-forward assisted STIRAP. J. Phys. Chem. A 119, 3479 (2015)
Chen, X., Muga, J.G.: Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator. Phys. Rev. A 82, 053403 (2010)
Chen, X., Torrontegui, E., Stefanatos, D., Li, J.S., Muga, J.G.: Optimal trajectories for efficient atomic transport without final excitation. Phys. Rev. A 84, 043415 (2011)
del Campo, A.: Fast frictionless dynamics as a toolbox for low-dimensional Bose–Einstein condensates. Eur. Phys. Lett. 96, 60005 (2011)
Schaff, J.F., Song, X.L., Vignolo, P., Labeyrie, G.: Fast optimal transition between two equilibrium states. Phys. Rev. A 82, 033430 (2010)
Chen, X., Muga, J.G.: Engineering of fast population transfer in three-level systems. Phys. Rev. A 86, 033405 (2012)
Santos, A.C., Silva, R.D., Sarandy, M.S.: Shortcut to adiabatic gate teleportation. Phys. Rev. A 93, 012311 (2016)
Hen, I.: Quantum gates with controlled adiabatic evolutions. Phys. Rev. A 91, 022309 (2015)
Deffner, S., Jarzynski, C., del Campo, A.: Classical and quantum shortcuts to adiabaticity for scale-invariant driving. Phys. Rev. X 4, 021013 (2014)
del Campo, A.: Frictionless quantum quenches in ultracold gases: a quantum dynamical microscope. Phys. Rev. A 84, 031606(R) (2011)
Song, X.K., Zhang, H., Ai, Q., Qiu, J., Deng, F.G.: Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm. New J. Phys. 18, 023001 (2016)
Wu, Q.C., Chen, Y.H., Huang, B.H., Shi, Z.C., Song, J., Xia, Y.: Protecting quantum state in time-dependent decoherence-free subspaces without the rotating-wave approximation. Ann. Phys. 529, 1700186 (2017)
Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Zheng, S.B.: Improving shortcuts to non-hermitian adiabaticity for fast population transfer in open quantum systems. Ann. Phys. 530, 1700247 (2017)
Kang, Y.H., Chen, Y.H., Huang, B.H., Song, J., Xia, Y.: Invariant-based pulse design for three-level systems without the rotating-wave approximation. Ann. Phys. 529, 1700004 (2017)
Kang, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Fast and robust quantum information transfer in annular and radial superconducting networks. Ann. Phys. 529, 1700154 (2017)
Friedman, J.R., Patel, V., Chen, W., Tolpygo, S.K., Lukens, J.E.: Quantum superposition of distinct macroscopic states. Nature 406, 43 (2000)
Zhou, Z., Chu, S.I., Han, S.: Quantum computing with superconducting devices: a three-level SQUID qubit. Phys. Rev. B 66, 054527 (2002)
Chen, Y.H., Shi, Z.C., Xia, Y., Zheng, S.B.: Optimal shortcut approach based on an easily obtained intermediate Hamiltonian. Phys. Rev. A 95, 062319 (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)
Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: Hybrid quantum circuits. Rev. Mod. Phys. 85, 623 (2013)
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 (2009)
Yang, C.P., Chu, S.I., Han, S.: Efficient scheme for quantum entanglement, quantum information transfer, and quantum gate with three-level SQUID qubits in cavity QED. arXiv:quant-ph/0305130
Acknowledgements
The authors thank Dr. Ye-Hong Chen, Dr. Bi-Hua Huang, and Dr. Du Ran for many fruitful discussions and very useful comments. This work was supported by the National Natural Science Foundation of China under Grants Nos. 11575045, 11374054 and 11674060.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ma, Lh., Kang, YH., Shi, ZC. et al. Shortcuts to adiabatic for implementing controlled-not gate with superconducting quantum interference device qubits. Quantum Inf Process 17, 292 (2018). https://doi.org/10.1007/s11128-018-2056-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-018-2056-x