Abstract
In this paper, we propose a scheme to generate a Fredkin gate in a single step based on path engineering. The quantum Zeno dynamics is utilized to simplify the Hamiltonian. As a result, an effective Hamiltonian will be obtained to drive the system to evolve into the target state in a short time if reasonable parameters are set. In addition, the results of explicit numerical simulations indicate that the scheme is robust against the instability of experimental parameters and the decoherence arising from atomic spontaneous emission and cavity decay. Most importantly, our scheme is just a single step, which greatly simplifies actual operation.








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Wright, K., Beck, K.M., Debnath, S., et al.: Benchmarking an 11-qubit quantum computer. Nat. Commun. 10, 5464 (2019)
Figgatt, C., Ostrander, A., Linke, N.M., et al.: Parallel entangling operations on a universal ion-trap quantum computer. Nature 572, 368 (2019)
Behera, B.K., Reza, T., Gupta, A., et al.: Designing quantum router in IBM quantum computer. Quantum Inf Process 18, 328 (2019)
You, J.Q., Tsai, J.S., Nori, F.: Scalable quantum computing with Josephson charge qubits. Phys. Rev. Lett. 89, 197902 (2002)
Wei, L.F., Nori, F.: An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb-Dicke limit. Phys. Lett. A 320, 131 (2003)
Tanamoto, T., Liu, Y., Hu, X., Nori, F.: Efficient quantum circuits for one-way quantum computing. Phys. Rev. Lett. 102, 100501 (2009)
Wei, L.F., Johansson, J.R., Cen, L.X., Ashhab, S., Nori, F.: Controllable coherent population transfers in superconducting qubits for quantum computing. Phys. Rev. Lett. 110, 113601 (2008)
You, J.Q., Wang, X., Tanamoto, T., Nori, F.: Efficient one-step generation of large cluster states with solid-state circuits. Phys. Rev. A 75, 052319 (2007)
Tashima, T., Tame, M.S., Ozdemir, S.K., Nori, F., Koashi, M., Weinfurter, H.: Photonic multipartite entanglement conversion using nonlocal operations. Phys. Rev. A 94, 052309 (2016)
Ashhab, S., Groot, P.C.D., Nori, F.: Speed limits for quantum gates in multiqubit systems. Phys. Rev. A 85, 052327 (2012)
Wei, L.F., Liu, Y., Storcz, M.J., Nori, F.: Macroscopic Einstein–Podolsky–Rosen pairs in superconducting circuits. Phys. Rev. A 73, 052307 (2006)
Groot, P.C.D., Ashhab, S., Lupascu, A., et al.: Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates. New J. Phys. 14, 073038 (2012)
Huang, Y.Y., Wu, Y.K., Wang, F., et al.: Experimental realization of robust geometric quantum gates with solid-state spins. Phys. Rev. Lett. 122, 010503 (2019)
Liu, B.J., Song, X.K., Xue, Z.Y., Wang, X., Yung, M.H.: Plug-and-play approach to nonadiabatic geometric quantum gates. Phys. Rev. Lett. 123, 100501 (2019)
Tan, T.R., Gaebler, J.P., Lin, Y., Wan, Y., Bowler, R., Leibfried, D., Wineland, D.J.: Multi-element logic gates for trapped-ion qubits. Nature 528, 380 (2009)
Tang, S.Q., Zhang, D.Y., Xie, L.J., Zhan, X.G., Gao, F.: Selective atom-cavity interaction scheme for quantum controlled-NOT gate using four-level atoms in cavity QED system. Commun. Theor. Phys. 51, 247 (2009)
Rosenblum, S., Gao, Y.Y., Reinhold, P., et al.: A CNOT gate between multiphoton qubits encoded in two cavities. Nat. Commu. 9, 652 (2008)
Cesa, A., Martin, J.: Two-qubit entangling gates between distant atomic qubits in a lattice. Phys. Rev. A 95, 052330 (2017)
Chuang, I.L., Yamamoto, Y.: Quantum bit regeneration. Phys. Rev. Lett. 76, 4281 (1996)
Cory, D.G., Price, M.D., Maas, W., Knill, E., Laflamme, R., Zurek, W.H., Havel, T.F., Somaroo, S.S.: Experimental quantum error correction. Phys. Rev. Lett. 81, 2152 (1998)
Hofmann, H.F.: Weak values emerge in joint measurements on cloned quantum systems. Phys. Rev. Lett. 109, 020408 (2012)
Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001)
Horn, R.T., Babichev, S.A., Marzlin, K.P., Lvovsky, A.I., Sanders, B.C.: Single-qubit optical quantum fingerprinting. Phys. Rev. Lett. 95, 150502 (2005)
Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv:quant-ph/0105032 [quant-ph]
Chau, H.F., Wilczek, F.: Simple realization of the Fredkin gate using a series of two-body operators. Phys. Rev. Lett. 75, 748 (1995)
Smolin, J.A., DiVincenzo, D.P.: Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate. Phys. Rev. A 53, 2855 (1996)
Gong, Y.X., Guo, G.C., Ralph, T.C.: Methods for a linear optical quantum Fredkin gate. Phys. Rev. A 78, 012305 (2008)
Shi, Z.C., Xia, Y., Song, J., Song, H.: One-step implementation of the Fredkin gate via quantum Zeno dynamics. Quantum Inf. Process. 12, 0215 (2012)
Liu, T., Guo, B.Q., Yu, C.S., Zhang, W.N.: One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications. Opt. Eepress. 46, 4498 (2018)
Sun, G.Q., Wu, J.L., Niu, W., Yu, W.R., Ji, X.: Remote implementation of a Fredkin gate via virtual excitation of an atom-cavity-fiber system. Ann. Phys. (Berlin) 532, 1900372 (2019)
Berry, M.V.: Transitionless quantum driving. J. Phys. A Math. Theor. 42, 365303 (2009)
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)
Facchi, P., Gorini, V., Marmo, G., Pascazio, S., Sudarshan, E.C.G.: Quantum Zeno dynamics. Phys. Lett. A 275, 12 (2000)
Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)
Huang, X.B., Zhong, Z.R., Chen, Y.H.: Generation of multi-atom entangled states in coupled cavities via transitionless quantum driving. Quantum Inf. Process. 14, 4475 (2016)
Shan, W.J., Xia, Y., Chen, Y.H., Song, J.: Fast generation of N-atom Greenberger–Horne–Zeilinger state in separate coupled cavities via transitionless quantum driving. Quantum Inf. Process. 15, 2359 (2016)
Chen, Z., Chen, Y.H., Xia, Y., Song, J., Huang, B.H.: Fast generation of three-atom singlet state by transitionless quantum driving. Sci. Rep. 6, 22202 (2016)
Wu, J.L., Ji, X., Zhang, S.: Fast generations of tree-type three-dimensional entanglement via Lewis–Riesenfeld invariants and transitionless quantum driving. Sci. Rep. 6, 33669 (2016)
Zhang, C.L., Luo, C.L., Liu, W.W.: Fast implementation of four-dimensional entangled state via transitionless quantum driving. Opt. Commun. 427, 497 (2018)
Zhang, C.L., Liu, W.W.: Fast implementation of quantum phase gates and creation of cluster states via transitionless quantum driving. Int. J Theor. Phys. 57, 2373 (2018)
Zhang, F.Y., Li, W.L., Yan, W.B., Xia, Y.: Speeding up adiabatic state conversion in optomechanical systems. J Phys. B At. Mol. Opt. Phys. 52, 115501 (2019)
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, Y.H., Shi, Z.C., Song, J., Xia, Y., Zheng, S.B.: Optimal shortcut approach based on an easily obtained intermediate Hamiltonian. Phys. Rev. A 95, 062319 (2017)
Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Song, J.: Reverse engineering of a Hamiltonian by designing the evolution operators. Sci. Rep. 6, 30151 (2016)
Kang, Y.H., Chen, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm. Phys. Rev. A 96, 022304 (2017)
Zheng, R.H., Kang, Y.H., Shi, Z.C., Xia, Y.: Complete and nondestructive atomic Bell-State analysis assisted by inverse engineering. Ann. Phys. (Berlin) 530, 1800133 (2018)
Shan, W.J., Zhang, X.P., Wang, W.Q., Lin, M.: Fast and robust generation of singlet state via shortcuts to adiabatic passage. Quantum Inf. Process. 18, 22 (2019)
Yu, W.R., Ji, X.: Fast preparing W state via a chosen path shortcut in circuit QED. Quantum Inf. Process. 18, 247 (2019)
Steck, D.A.: Rubidium 87 D line data. http://steck.us/alkalidata
Mundt, A.B., Kreuter, A., Becher, C., Leibfried, D., Eschner, J., Schmidt, K.F., Blatt, R.: Coupling a single atomic quantum bit to a high finesse optical cavity. Phys. Rev. Lett. 89, 103001 (2002)
Spillane, S.M., Kippenberg, T.J., Vahala, K.J., Goh, K.W., Wilcut, E., Kimble, H.J.: Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)
Buck, J.R., Kimble, H.J.: Optimal sizes of dielectric microspheres for cavity QED with strong coupling. Phys. Rev. A 67, 033806 (2003)
Hartmann, M.J., Brandao, F.G.S.L., Plenio, M.B.: Strongly correlated polaritons in a two-dimensional array of cavities. Nat. Phys. 2, 849 (2006)
You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58, 42 (2005)
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)
Wendin, G.: Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017)
You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature (London) 474, 589 (2011)
Yamamoto, T., Inomata, K., Koshino, K., Billangeon, P.M., Nakamura, Y., Tsai, J.S.: Superconducting flux qubit capacitively coupled to an LC resonator. New J. Phys. 16, 015017 (2014)
Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., García-Ripoll, J.J., Zueco, D., Hummer, T., Solano, E., Marx, A., Gross, R.: Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nat. Phys. 6, 772 (2010)
Peropadre, B., Forn-Díaz, P., Solano, E., García-Ripoll, J.J.: Switchable Ultrastrong Coupling in Circuit QED. Phys. Rev. Lett. 105, 023601 (2010)
Yuan, X., Liu, K., Xu, Y., Wang, W.T., Ma, Y.W., Zhang, F., Yan, Z.P., Luyan Sun, L.Y., Ma, X.F.: Experimental quantum randomness processing using superconducting qubits. Phys. Rev. Lett. 117, 010502 (2016)
Gu, X., Kockum, A.F., Miranowicz, A., Liu, Y.X., Nori, F.: Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1 (2017)
Vepsalainen, A., Danilin, S., Paraoanu, G.S.: Superadiabatic population transfer in a three-level superconducting circuit. Sci. Adv. 5, eaau5999 (2019)
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grants Nos. 61275215 and 11674059, the Natural Science Foundation of Fujian Province of China under Grants Nos. 2016J01009 and 2016J01008, and the Educational Committee of Fujian Province of China under Grants No. JAT190978.
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Zhang, CL., Liu, WW. & Lin, XM. One-step implementation of a robust Fredkin gate based on path engineering. Quantum Inf Process 19, 265 (2020). https://doi.org/10.1007/s11128-020-02767-6
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DOI: https://doi.org/10.1007/s11128-020-02767-6