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Quantum phase gate is a necessary quantum component for quantum coding and quantum computing. Compared with the traditional gate circuit, quantum phase gate has the characteristics of unitarity and reversibility. Therefore, we construct a model of mutual coupling between a single Λ -type three-level atom and two superconducting resonators, which is connected by a capacitor. By separately controlling the disconnection time and connection time of the two superconducting resonators in the model as well as by controlling the magnetic flux of the superconducting quantum interference device (SQUID) to make a certain transition energy level of the Λ -type three-level atom equal the relevant resonance energy level, the interaction between the two levels can be achieved and the system can be manipulated. Afterwards, we propose four control schemes for implementing the controlled-Z gate through a three-step operation, and two operation schemes for implementing swap gate through a four-step operation. At the same time, the numerical simulations of fidelity are implemented for the first operation scheme for controlling the Z-gate. The results of fidelity discussion show that the fidelity of this scheme is 96.67% through the running time of 20.83 ns, thus it proves that this scheme is theoretically feasible. The increase in the three attenuation parameters, i.e., attenuation rate, relaxation rate, and phase shift ratio, will reduce the fidelity of the system, while the increase in coupling strength will cut down the time of system operation, thus reducing the influence of attenuation parameters and improving the system fidelity.In this paper we present a quantum phase gate scheme in which two superconducting resonators and a Λ -type three-level atom are coupled with two capacitors. Since the experimental setup is simplified, it is important to reduce the coherence between devices. In addition, the solution has no restriction on the strength of the classic pulse principally, through which the system operates faster and the fidelity of the phase gate is improved effectively.
[1] Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 (in Chinese)[任宝藏, 邓富国 2015 64 160303]
[2] Li M, Chen Y, Guo G C, Ren X F 2017 Acta Phys. Sin. 66 144202 (in Chinese)[李明, 陈阳, 郭光灿, 任希峰 2017 66 144202]
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[4] Sleator T, Weinfurter H 1995 Phys. Rev. Lett. 74 4087
[5] Yang C P, Han S 2005 Phys. Rev. A 72 032311
[6] Peng J, Wu Y W, Li X J 2011 Acta Phot. Sin. 40 466 (in Chinese)[彭俊, 邬云文, 李小娟 2011 光子学报 40 466]
[7] You J Q, Nori F 2011 Nature 474 589
[8] Xiang Z L, Ashhab S, You J Q, Nori F 2013 Rev. Mod. Phys. 85 623
[9] Barends R, Kelly J, Megrant A, Sank D, Jeffrey E 2013 Phys. Rev. Lett. 111 080502
[10] Clarke J, Wilhelm F K 2008 Nature 453 1031
[11] Filipp S, Maurer P, Leek P J, et al. 2009 Phys. Rev. Lett. 102 200402
[12] Reed M D, Carlo L D, Johnson B R, Sun L, Schuster D I 2010 Phys. Rev. Lett. 105 173601
[13] Yang C P, Chu S I, Han S 2003 Phys. Rev. A 67 042311
[14] Majer J, Chow J M, Gambetta J M, Johnson B R 2007 Nature 449 7161
[15] Dicarlo L, Chow J M, Gambetta J M, Bishop L B 2009 Nature 460 7252
[16] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[17] Yang C P, Chu S I, Han S 2004 Phys. Rev. Lett. 92 117902
[18] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S 2004 Nature 431 7005
[19] Chiorescu I, Bertet P, Semba K, Nakamura Y 2004 Nature 431 159
[20] Strauch F W 2012 Phys. Rev. Lett. 109 210501
[21] Leek P J, Filipp S, Maurer P, Baur M, Bianchetti R 2009 Phys. Rev. B 79 180511
[22] Strand J D, Ware M, Beaudoin F, Ohki T A, Johnson B R 2013 Phys. Rev. B 87 220505
[23] Hua M, Tao M J, Deng F G 2014 Phys. Rev. A 90 012328
[24] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[25] Su Q P, Yang C P, Zheng S B 2014 Sci. Rep. 4 3898
[26] Xiang Z L, Ashhab S, You J Q, Nori F 2013 Rev. Mod. Phys. 85 623
[27] Hoi I C, Wilson C M, Johansson G 2011 Phys. Rev. Lett. 107 073601
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[1] Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 (in Chinese)[任宝藏, 邓富国 2015 64 160303]
[2] Li M, Chen Y, Guo G C, Ren X F 2017 Acta Phys. Sin. 66 144202 (in Chinese)[李明, 陈阳, 郭光灿, 任希峰 2017 66 144202]
[3] Brune M, Hagley E, Dreyer J, et al. 1996 Phys. Rev. Lett. 77 4887
[4] Sleator T, Weinfurter H 1995 Phys. Rev. Lett. 74 4087
[5] Yang C P, Han S 2005 Phys. Rev. A 72 032311
[6] Peng J, Wu Y W, Li X J 2011 Acta Phot. Sin. 40 466 (in Chinese)[彭俊, 邬云文, 李小娟 2011 光子学报 40 466]
[7] You J Q, Nori F 2011 Nature 474 589
[8] Xiang Z L, Ashhab S, You J Q, Nori F 2013 Rev. Mod. Phys. 85 623
[9] Barends R, Kelly J, Megrant A, Sank D, Jeffrey E 2013 Phys. Rev. Lett. 111 080502
[10] Clarke J, Wilhelm F K 2008 Nature 453 1031
[11] Filipp S, Maurer P, Leek P J, et al. 2009 Phys. Rev. Lett. 102 200402
[12] Reed M D, Carlo L D, Johnson B R, Sun L, Schuster D I 2010 Phys. Rev. Lett. 105 173601
[13] Yang C P, Chu S I, Han S 2003 Phys. Rev. A 67 042311
[14] Majer J, Chow J M, Gambetta J M, Johnson B R 2007 Nature 449 7161
[15] Dicarlo L, Chow J M, Gambetta J M, Bishop L B 2009 Nature 460 7252
[16] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[17] Yang C P, Chu S I, Han S 2004 Phys. Rev. Lett. 92 117902
[18] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S 2004 Nature 431 7005
[19] Chiorescu I, Bertet P, Semba K, Nakamura Y 2004 Nature 431 159
[20] Strauch F W 2012 Phys. Rev. Lett. 109 210501
[21] Leek P J, Filipp S, Maurer P, Baur M, Bianchetti R 2009 Phys. Rev. B 79 180511
[22] Strand J D, Ware M, Beaudoin F, Ohki T A, Johnson B R 2013 Phys. Rev. B 87 220505
[23] Hua M, Tao M J, Deng F G 2014 Phys. Rev. A 90 012328
[24] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[25] Su Q P, Yang C P, Zheng S B 2014 Sci. Rep. 4 3898
[26] Xiang Z L, Ashhab S, You J Q, Nori F 2013 Rev. Mod. Phys. 85 623
[27] Hoi I C, Wilson C M, Johansson G 2011 Phys. Rev. Lett. 107 073601
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