Abstract
A scheme of fast synthesizing the Fredkin gate is proposed in cavity QED via quantum Zeno dynamics. Three atoms are trapped in three different but directly coupled cavities in this scheme. The strictly numerical simulations are given, and the influences of cavity decay and spontaneous emission on the gate operation are analyzed with master equation. The result shows that our scheme is robust against atomic spontaneous emission because of the large detuning. Since the atoms are separated in different cavities, it is easier to manipulate atoms experimentally.
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Buluta, I.M., Nori, F.: Quantum simulators. Science 326, 108 (2009)
Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86, 153 (2014)
Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling n qubits in a cavity or coupled to a resonator. Phys. Rev. A 81, 062323 (2010)
Yang, C.P., Zheng, S.B., Nori, F.: Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity. Phys. Rev. A 82, 062326 (2010)
Ashhab, S., de Groot, P.C., Nori, F.: Speed limits for quantum gates in multiqubit systems. Phys. Rev. A 85, 052327 (2012)
de Groot, P.C., Ashhab, S., Lupascu, A., DiCarlo, L., Nori, F., Harmans, C.J.P.M., Mooij, J.E.: Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates. New J. Phys. 14, 073038 (2012)
Zheng, S.B., Yang, C.P., Nori, F.: Arbitrary control of coherent dynamics for distant qubits in a quantum network. Phys. Rev. A 82, 042327 (2010)
Yang, C.P., Su, Q.P., Liu, J.M.: Proposal for realizing a multiqubit tunable phase gate of one qubit simultaneously controlling n target qubits using cavity QED. Phys. Rev. A 86, 024301 (2012)
Zheng, S.B.: Implementation of Toffoli gates with a single asymmetric Heisenberg XY interaction. Phys. Rev. A 87, 042318 (2013)
Chen, C.Y., Feng, M., Gao, K.L.: Toffoli gate originating from a single resonant interaction with cavity QED. Phys. Rev. A 73, 064304 (2006)
Lanyon, B.P., Barbieri, M., Almeida, M.P., Jennewein, T., Ralph, T.C., Resch, K.J., Pryde, G.J., O’Brien, J.L., Gilchrist, A., White, A.G.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134 (2009)
DiVincenzo, D.P.: Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015 (1995)
Xiao, Y.F., Zou, X.B., Guo, G.C.: Implementing a conditional N-qubit phase gate in a largely detuned optical cavity. Phys. Rev. A 75, 014302 (2007)
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)
Zou, X.B., Xiao, Y.F., Li, S.B., Yang, Y., Guo, G.C.: Quantum phase gate through a dispersive atom-field interaction. Phys. Rev. A 75, 064301 (2007)
Lin, G.W., Zou, X.B., Lin, X.M., Guo, G.C.: Robust and fast geometric quantum computation with multiqubit gates in cavity QED. Phys. Rev. A 79, 064303 (2009)
Monz, T., Kim, K., Hansel, 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)
Yang, W.L., Yin, Z.Q., Xu, Z.Y., Feng, M., Du, J.F.: One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity. Appl. Phys. Lett. 96, 241113 (2010)
Zou, X.B., Kim, J., Lee, H.W.: Generation of two-mode nonclassical motional states and a Fredkin gate operation in a two-dimensional ion trap. Phys. Rev. A 63, 065801 (2001)
Wang, B., Duan, L.M.: Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation. Phys. Rev. A 75, 050304 (2007)
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)
Zhang, X.L., Gao, K.L., Feng, M.: Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED. Phys. Rev. A 74, 024303 (2006)
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.: A proposal for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED. J. Phys. Condens. Matter. 23, 225702 (2011)
Shao, X.Q., Zheng, T.Y., Feng, X.L., Oh, C.H., Zhang, S.: One-step implementation of the genuine Fredkin gate in high-Q coupled three-cavity arrays. J. Opt. Soc. Am. B 31, 697 (2014)
Fiurás̆ek, J.: Linear optical Fredkin gate based on partial-SWAP gate. Phys. Rev. A 78, 032317 (2008)
Gong, Y.X., Guo, G.C., Ralph, T.C.: Methods for a linear optical quantum Fredkin gate. Phys. Rev. A 78, 012305 (2008)
Fiurás̆ek, J.: Linear-optics quantum Toffoli and Fredkin gates. Phys. Rev. A 73, 062313 (2006)
Misra, B., Sudarshan, E.C.G.: The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756763 (1977)
Cao, X., Ai, Q., Sun, C.P., Nori, F.: The transition from quantum Zeno to anti-Zeno effects for a qubit in a cavity by varying the cavity frequency. Phys. Lett. A 376, 349 (2012)
Ai, Q., Xu, D., Yi, S., Kofman, A.G., Sun, C.P., Nori, F.: Quantum anti-Zeno effect without wave function reduction. Sci. Rep. 3, 1752 (2013)
Zhang, W., Kofman, A.G., Zhuang, J., You, J.Q., Nori, F.: Quantum Zeno and anti-Zeno effects measured by transition probabilities. Phys. Lett. A 377, 1837 (2013)
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., Scardicchio, A., Schulman, L.S.: Zeno dynamics yields ordinary constraints. Phys. Rev. A 65, 012108 (2001)
Facchi, P., Pascazio, S.: Quantum Zeno and inverse quantum Zeno effects. Prog. Opt. 42, 147217 (2001)
Pachos, J., Walther, H.: Quantum computation with trapped ions in an optical cavity. Phys. Rev. Lett. 89, 187903 (2002)
Zhou, L., Yang, S., Liu, Y.X., Sun, C.P., Nori, F.: Quantum Zeno switch for single-photon coherent transport. Phys. Rev. A 80, 062109 (2009)
Pachos, J.K., Beige, A.: Decoherence-free dynamical and geometrical entangling phase gates. Phys. Rev. A 69, 033817 (2004)
Franson, J.D., Jacobs, B.C., Pittman, T.B.: Quantum computing using single photons and the Zeno effect. Phys. Rev. A 70, 062302 (2004)
You H., Franson, J.D.: Theoretical comparison of quantum Zeno gates and nonlinear phase gates. arXiv:1008.1513 (1–14)
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)
Zhang, S., Shao, X.Q., Chen, L., Zhao, Y.F., Yeon, K.H.: Robust \(\sqrt{swap}\) gate on nitrogen-vacancy centres via quantum Zeno dynamics. J. Phys. B At. Mol. Opt. Phys. 44, 075505 (2011)
Shi, Z.C., Xia, Y., Song, J., Song, H.S.: Atomic quantum state transferring and swapping via quantum Zeno dynamics. J. Opt. Soc. Am. B 28, 2909 (2011)
Wang, X.B., You, J.Q., Nori, F.: Quantum entanglement via two-qubit quantum Zeno dynamics. Phys. Rev. A 77, 062339 (2008)
Wen, A.L., Guang, Y.H.: Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics. Phys. Rev. A 83, 022322 (2011)
Shi, Z.C., Xia, Y., Song, J., Song, H.S.: Effective scheme for generation of two-dimensional cluster states via quantum Zeno dynamics. Eur. Phys. J. D 66, 11 (2012)
Shi, Z.C., Xia, Y., Song, J., Song, H.S.: One-step implementation of the Fredkin gate via quantum Zeno dynamics. Quan. Infor. Comput. 12, 0215 (2012)
You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58(11), 42 (2005)
You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature 474, 589 (2011)
Buluta, I., Ashhab, S., Nori, F.: Natural and artificial atoms for quantum computation. Rep. Prog. Phys. 74, 104401 (2011)
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)
Tanamoto, T., Maruyama, K., Liu, Y.X., Hu, X., Nori, F.: Efficient purification protocols using iSWAP gates in solid-state qubits. Phys. Rev. A 78, 062313 (2008)
Nori, F.: Quantum football. Science 325, 689 (2009)
Facchi, P., Marmo, G., Pascazio, S.: Quantum Zeno dynamics and quantum Zeno sub-spaces. J. Phys. Conf. Ser. 196, 012017 (2009)
Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)
Shao, X.Q., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Deterministic generation of arbitrary multi-atom symmetric Dicke states by a combination of quantum Zeno dynamics and adiabatic passage. Europhys. Lett. 90, 50003 (2010)
James, D.F., Jerke, J.: Effective Hamiltonian Theory and its applications in quantum information. Can. J. Phys. 85, 625 (2007)
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 (2012)
Tan, Sze M.: A computational toolbox for quantum and atomic optics. J. Opt. B 1, 424 (1999)
Spillane, S.M., Kippenberg, T.J., Painter, O.J., Vahala, K.J.: Ideality in a fibertTaper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett. 91, 043902 (2003)
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)
Zheng, S.B.: Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities. Phys. Lett. A 94, 154101 (2009)
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 11105030, the Natural Science Foundation of Fuzhou University of China under Grant No. XRC-0976 and No. 2010-XQ-28, the funds from Education Department of Fujian Province of China under Grant Nos. JA11005, JA10009 and JA10039, the National Natural Science Foundation of Fujian Province of China under Grant Nos. 2010J01006 and 2012J01269, the Foundation of Ministry of Education of China under Grant No. 212085.
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Song, LC., Xia, Y. & Song, J. Experimentally optimized implementation of the Fredkin gate with atoms in cavity QED. Quantum Inf Process 14, 511–529 (2015). https://doi.org/10.1007/s11128-014-0884-x
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DOI: https://doi.org/10.1007/s11128-014-0884-x