双模腔中强场驱动下的非传统几何逻辑门
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摘要
20世纪80年代以来,人们逐渐发现,信息论、计算机科学和物理学之间不仅表现出应用上的联系,而且这些科学概念、原理都要受到基本物理规律的制约。在经典信息中,信息由比两个独立的态编码,一般称编码态为比特。但是,量子态却可以在两个编码态中连续变化。因此,当信息由量子态编码时,传统的信息框架已经从本质上发生了改变。量子信息,一个暂新的学科从而被提出并发展起来应用量子态以处理信息的存储、运输及计算等。一般而言,量子信息学包含量子通讯和和量子计算。这个新兴学科拓展了科研的内容,极大地丰富和加深了人们对微观世界的认识和理解,体现出巨大的应用前景。在量子信息领域中,腔量子电动力学(QED)方案被认为是最有效的实现、存储和传递信息的方案之一。随着研究的进一步深入和技术的发展,越来越多的量子信息处理过程可通过腔QED方案在实验上实现。
本文首先介绍了目前四种量子逻辑门的实验方案,它们是腔QED,离子阱技术,核磁共振技术和量子点。本文的工作将集中在腔QED,于是我们系统地评述了腔QED的基础理论,并且介绍了量子信息中的几何相位及其在腔QED中的应用。通过对双模腔中强场驱动下的非传统几何逻辑门的研究,我们的工作主要有如下三方面:1)在双模腔中,强的共振经典场驱动下,通过限制在腔QED中的两个三能级原子建立二量子比特,提出了非传统几何逻辑门的方案; 2)由于腔的退相干会导致腔模的起伏,并因此导致保真度的降低。我们采用了双哈密顿量的方法,有效的防止了这种有害的效应,提高了保真度;3)在方案处于腔模退相干情况下建立一个π-相位门,并在不同的周期参量下,对选通时间、保真度、成功率等进行了数值计算,证明了本文的方案具有选通时间短,保真度及成功率高等优势。
双模腔中强场驱动下的非传统几何逻辑门的量子编码能级直接与激光或腔场耦合,从而对激光束的需求量更少,降低了实验难度。并由于较小的去谐量,可以更快的完成逻辑门的操作。
Since the 1980s, scientists gradually realized that information theory, computer science and physics are correlated to each other in application. Moreover, physics principles plays fundamental role in unprecedented way in information theory. In classical sense of information, the information is encoded in simply two distinct states, usually called as a bit. However, quantum state can change continuously from these two states. It is therefore understandable that when the information is encoded into quantum states, the traditional framework of the information has a fundamental change. This is why a new discipline known as quantum information had been put forwarded and has been built up in order to deal with the information storage, transfer and calculation etc. with quantum states. Generally speaking, quantum information includes quantum communication and quantum computation. Quantum information has been greatly widened the horizon of science research, enriched and deepened our understanding of the microcosm, and also has demonstrated the remarkably potential application. In the realm of quantum information,cavity Quantum Electrodynamics (QED) is considered as one of the most effective scheme to realize, storage and transfer the quantum information. With the development of the science and technology, more and more quantum information techniques can be realized in experiment through the cavity QED scheme.
This dissertation starts with introduction of four main experiment schemes in quantum information; and they are cavity-QED, ion trap, nuclear magnetic resonance and quantum dot. Since our work concentrates on the cavity-QED, so we introduce the basic theory of cavity-QED and the geometric phase in quantum information with its application in the cavity-QED. Then we present our research in detail on the strong-driving-assisted unconventional geometric logic gating in a two-mode cavity. The principal results obtained are summarized in the following three aspects: 1) We propose a candidate two-qubit unconventional geometric quantum gates on two identical three-level atoms in a two-mode cavity, strongly driven by a resonant classical field; 2) We have employed the double-Hamiltonian method to eliminate the cavity mode fluctuations due to the decay, so the fidelity in our approach is higher than in some other ones; 3) We built aπ-phase gate under the influence from the cavity decay. By numerical calculations with adopting the real values of physical parameters from microwave cavity experiments in different periodic situations, we studied the influence of the gating time, fidelity and success probability. Results show that our approach is advantageous for it has smaller gating time, higher fidelity and larger success probability.
As the qubit-encoded levels are directly coupled by a laser or the cavity modes, our model involves less laser beams, which would reduce the experimental difficulty. Due to the small detuning, our gate could be carried out faster than others.
本文首先介绍了目前四种量子逻辑门的实验方案,它们是腔QED,离子阱技术,核磁共振技术和量子点。本文的工作将集中在腔QED,于是我们系统地评述了腔QED的基础理论,并且介绍了量子信息中的几何相位及其在腔QED中的应用。通过对双模腔中强场驱动下的非传统几何逻辑门的研究,我们的工作主要有如下三方面:1)在双模腔中,强的共振经典场驱动下,通过限制在腔QED中的两个三能级原子建立二量子比特,提出了非传统几何逻辑门的方案; 2)由于腔的退相干会导致腔模的起伏,并因此导致保真度的降低。我们采用了双哈密顿量的方法,有效的防止了这种有害的效应,提高了保真度;3)在方案处于腔模退相干情况下建立一个π-相位门,并在不同的周期参量下,对选通时间、保真度、成功率等进行了数值计算,证明了本文的方案具有选通时间短,保真度及成功率高等优势。
双模腔中强场驱动下的非传统几何逻辑门的量子编码能级直接与激光或腔场耦合,从而对激光束的需求量更少,降低了实验难度。并由于较小的去谐量,可以更快的完成逻辑门的操作。
Since the 1980s, scientists gradually realized that information theory, computer science and physics are correlated to each other in application. Moreover, physics principles plays fundamental role in unprecedented way in information theory. In classical sense of information, the information is encoded in simply two distinct states, usually called as a bit. However, quantum state can change continuously from these two states. It is therefore understandable that when the information is encoded into quantum states, the traditional framework of the information has a fundamental change. This is why a new discipline known as quantum information had been put forwarded and has been built up in order to deal with the information storage, transfer and calculation etc. with quantum states. Generally speaking, quantum information includes quantum communication and quantum computation. Quantum information has been greatly widened the horizon of science research, enriched and deepened our understanding of the microcosm, and also has demonstrated the remarkably potential application. In the realm of quantum information,cavity Quantum Electrodynamics (QED) is considered as one of the most effective scheme to realize, storage and transfer the quantum information. With the development of the science and technology, more and more quantum information techniques can be realized in experiment through the cavity QED scheme.
This dissertation starts with introduction of four main experiment schemes in quantum information; and they are cavity-QED, ion trap, nuclear magnetic resonance and quantum dot. Since our work concentrates on the cavity-QED, so we introduce the basic theory of cavity-QED and the geometric phase in quantum information with its application in the cavity-QED. Then we present our research in detail on the strong-driving-assisted unconventional geometric logic gating in a two-mode cavity. The principal results obtained are summarized in the following three aspects: 1) We propose a candidate two-qubit unconventional geometric quantum gates on two identical three-level atoms in a two-mode cavity, strongly driven by a resonant classical field; 2) We have employed the double-Hamiltonian method to eliminate the cavity mode fluctuations due to the decay, so the fidelity in our approach is higher than in some other ones; 3) We built aπ-phase gate under the influence from the cavity decay. By numerical calculations with adopting the real values of physical parameters from microwave cavity experiments in different periodic situations, we studied the influence of the gating time, fidelity and success probability. Results show that our approach is advantageous for it has smaller gating time, higher fidelity and larger success probability.
As the qubit-encoded levels are directly coupled by a laser or the cavity modes, our model involves less laser beams, which would reduce the experimental difficulty. Due to the small detuning, our gate could be carried out faster than others.
引文
[1] R Feynman. Simulating physics with computers. Internat J Theoret Phys, 1982,21(6):467-488
[2] P Benioff. The computer as a physical system-a microscopic quantum mechanical hamiltonian model of computers as represented by turing machines. Phys Rev Lett, 1980,(22):563-591
[3] C H Bennett. Quantum cryptography using any two nonorthogonal states. Phys Rev Lett, 1992,68:3121
[4] A K Ekert. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991,67:661
[5] T Schaetz, M. D. Barrett, et al. Quantum Dense Coding with Atomic Qubits. Phys Rev Lett, 2004,93(4):040505
[6] X Y Li, K C Peng, et al. Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam. Phys Rev Lett, 2002,88(4):047904
[7] John H R and N F Johnson. Multipartite entangled coherent states. Phys Rev A, 2002,63:012303
[8] J Cho, H W Lee. Quantum teleportation with atoms trapped in cavities. Phys Rev A, 2004,70:034305
[9] D Deutsch. Quantum theory—the Church-Turing principle and the universal quantum computer. Proc of Roy Soc London A, 1985,400:97～117
[10] T Pellizzari, Gardiner S A, J I Cirac, et al. Decoherence continuous observation and quantum computing a cavity QED model. Phys Rev Lett, 1995,75:3788～3791
[11] Zheng S B, Guo G C. Eficient scheme for two—atom entanglement and quantum information processing in cavity QED. Phys Rev Lett, 2000, 85:2392—2395
[12] Grover L K. Algorithms for quantum computation:discrete logarithms and factoring[C].In:Proceedings of the 35th Annual Symposium on Foundations of Computer Science. Piscataway NJ IEEE Press, 1994,24124-134.
[13] Shor P W. Quantum computing.documenta mathematica. Proceedings of the International Congress of Mathematicians, Berlin, Germany, 1998,467-486
[14] Cirac J I, Zoller P. Quantmn computations with cold trapped ions. Phys Rev Lett, 1995,74:4091—4094
[15] Sleane A. The ion trap quantum information processor. Appl Phys B, 1997,64: 623
[16] Gershenfield N A, Chuang I L. Bulk spin-resonance quantum computation, Science,1997,275:350.
[17] Cory D G, Fahmy A F, Havel T F. Ensemble quantum computing by NMR spectroscopy. Proc.Nat1.Acad.Sci.USA, 1997,94:1634
[18] Jones J A, Mosca M, Hansen R H. Implementation of a quantum search algorithm on a quantum computer. Nature, 1998,393:344—346
[19] DiVicenzo D P, Bacon D, Kempe J, et a1.Universal quantum computation with the exchange interaction. Nature, 2000,408:339
[20] Kikkawa J M, Smorchkova I P, Samarth N, et a1.Room temperature spin memory in two-dimensional electron Gases. Science, 1997,277:1284
[21] Imamoglu A, Awschalom D D, Burkard G, et a1. Quantum information processing using quantum dot spins andcavity QED. Phys Rev Lett, 1999,83:4204-4207
[22] M Brune, P Nussenzveig, F Schmidt-Kaler, et al. From Lamb shift to light shifts:vacuum and subphoton cavity fields measured by atomic phasesensitive detection. Phys Rev Lett, 1994,72:3339-3342
[23] Turchette Q A, Hood C J, Lange W, et a1.Measurement of conditional phase shifts for quantum logic. Phys Rev Lett, 1995,75:4710—4713
[24] S. Haroche, M. Brune, J.M. Raimond. Manipulation of optical fields by atomic interferometry:quantum variations on a theme by Young. Appl Phys B, 1992,54:355
[25] M Brune, F S Kaler, A Maali, et al. Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity. Phys Rev Lett, 1996,76:1800
[26] E. T. Jaynes, F. W. Cummings. Comparision of quantum and semiclassical radiation theories with application to the beam maser. Proc IEEE, 1963,51:89
[27] H Rauch, A Zeilinger, G Badurek, et al. Comment on Neutron Interferometric Observation of Noncyclic Phase, Phys Lett A, 1975,54:425
[28] E Solano, G S Agarwal, and H Walther. Strong-driving-assisted multipartite entanglement in cavity QED. Phys Rev Lett, 2003,90:027903
[29] 曹卓良. 量子信息中的腔QED技术.量子电子学报,2004,21(2): 243-256
[30] Guo G P, Li C F, Li J, et al. Scheme for the preparation of multiparticle entanglement in cavity QED. Phys Rev A , 2002,65: 042102
[31] M V Berry. Quantal phase factors accompanying adiabatic changes. Proc R Soc London, 1984,392: 45
[32] P W Shor. Scheme for reducing decoherence in quantum computer memory. Phys Rev A, 1995,52:2493
[33] A M Steane. Error Correcting Codes in Quantum Theory. Phys Rev Lett, 1996,77:793
[34] A M Steane. Overhead and noise threshold of fault-tolerant quantum error correction. Phys Rev A, 2003,68:042322
[35] P Zanardi, M Rasetti. Noiseless quantum codes. Phys Rev Lett, 1997,79:3306
[36] P Zanardi, M Rasetti. Quantum computation based on non-abelian phases. Phys Lett A, 1999,264:94
[37] J Pachos, P Zanardi, and M Rasetti. Non-Abelian Berry connections for quantum computation. Phys Rev A, 2000,61(R):010305
[38] J Pachos, H Walther. Quantum computation with trapped ions in an optical cavity. Phys Rev Lett, 2002,89:187903
[39] G Falci, R Fazio, G M Palma, et al. Detection of geometric phases in superconducting nanocircuits. Nature, 2000,407:355
[40] L M Duan, J I Cirac, P Zoller. Geometric manipulation of trapped ions for quantum Computation. Science, 2001,292:1695-1697
[41] J A Jones, V Vedral, A Ekert, et al. A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field. Nature, 1999,403:869
[42] J J Garcia-Ripoll, J I Cirac. Quantum Computation with Unknown Parameters. Phys Rev Lett, 2003,90:127902
[43] X B Wang and M Keiji. Non-adiabatic conditional geometric phase shift with NMR. Phys Rev Lett, 2001,87:097901
[44] S L Zhu, Z D Wang. Unconventional geometric quantum computation. Phys Rev Lett, 2003,91:187902
[45] S B Zheng. Unconventional geometric quantum phase gates with a cavity QED system. Phys Rev A, 2004,70:052320
[46] Y Aharonov and J Anandan. Phase Change during a Cyclic Quantum Evolution. Phys Rev Lett, 1987,58:1593
[47] J Samuel, R Bhandari. General Setting for Berry's Phase. Phys Rev Lett, 1988,60:2339
[48] S L Zhu, Z D Wang, and Y D Zhang. Nonadiabatic noncyclic geometric phase of a spin-1 / 2 particle subject to an arbitrary magnetic field. Phys Rev B, 2000,61:1142
[49] S L Zhu and Z D Wang. Nonadiabatic Monocyclic Geometric Phase and EnsembleAverage Spectrum of Conductance in Disordered Mesoscopic Rings with Spin-Orbit Coupling. Phys Rev Lett, 2000,85:1076
[50] D Leibfried, B De Marco, V Meyer, et al. Experimental demonstration of a robust high-fidelity geometric two ionqubit phase gate. Nature, 2003,422:412
[51] A Luis. Geometric phase in a flat space for electromagnetic scalar waves. J Phys A, 2001,34:7677
[52] X Wang and P Zanardi. Multipartite entangled coherent states. Phys Rev A, 2002,65:032327
[53] C Y Chen, X L Zhang, Z J Deng, et al. Influence from cavity decay on geometric quantum computation in the large-detuning cavity QED model. Phys Rev A, 2006,74:032328
[54] X L Feng, Z Wang, C Wu, et al. Scheme for unconventional geometric quantum computation in cavity QED. Phys Rev A, 2007,75:052312
[55] C Y Chen, M Feng, X L Zhang, et al. Strong-driving-assisted unconventional geometric logic gate in cavity QED. Phys Rev A, 2006,73:032344
[56] X L Feng, Z S Wang, C F Wu, et al. Scheme for unconventional geometric quantum computation in cavity QED. Phys Rev A, 2007,75:052312
[57] S B Zheng. Quantum Logic Gates for Hot Ions without a Speed Limitation. Phys Rev Lett, 2006,90:217901
[58] M Hennrich, T Legero, A Kuhn, et al. Vacuum-Stimulated Raman Scattering Based on Adiabatic Passage in a High-Finesse Optical Cavity. Phys Rev Lett, 2000,85:4872
[59] J K Pachos and A Beige. Decoherence-free dynamical and geometrical entangling phase gates. Phys Rev A, 2004,69:0338l7
[60] P Solinas, P Zanardi, N Zanghi, et al. Semiconductor-based geometrical quantum gates. Phys Rev B, 2003,67:121307
[61] A Rauschenbeutel, G Nogues, S Osnaghi, et al. Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED. Phys Rev Lett, 1999,83:5166
[2] P Benioff. The computer as a physical system-a microscopic quantum mechanical hamiltonian model of computers as represented by turing machines. Phys Rev Lett, 1980,(22):563-591
[3] C H Bennett. Quantum cryptography using any two nonorthogonal states. Phys Rev Lett, 1992,68:3121
[4] A K Ekert. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991,67:661
[5] T Schaetz, M. D. Barrett, et al. Quantum Dense Coding with Atomic Qubits. Phys Rev Lett, 2004,93(4):040505
[6] X Y Li, K C Peng, et al. Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam. Phys Rev Lett, 2002,88(4):047904
[7] John H R and N F Johnson. Multipartite entangled coherent states. Phys Rev A, 2002,63:012303
[8] J Cho, H W Lee. Quantum teleportation with atoms trapped in cavities. Phys Rev A, 2004,70:034305
[9] D Deutsch. Quantum theory—the Church-Turing principle and the universal quantum computer. Proc of Roy Soc London A, 1985,400:97～117
[10] T Pellizzari, Gardiner S A, J I Cirac, et al. Decoherence continuous observation and quantum computing a cavity QED model. Phys Rev Lett, 1995,75:3788～3791
[11] Zheng S B, Guo G C. Eficient scheme for two—atom entanglement and quantum information processing in cavity QED. Phys Rev Lett, 2000, 85:2392—2395
[12] Grover L K. Algorithms for quantum computation:discrete logarithms and factoring[C].In:Proceedings of the 35th Annual Symposium on Foundations of Computer Science. Piscataway NJ IEEE Press, 1994,24124-134.
[13] Shor P W. Quantum computing.documenta mathematica. Proceedings of the International Congress of Mathematicians, Berlin, Germany, 1998,467-486
[14] Cirac J I, Zoller P. Quantmn computations with cold trapped ions. Phys Rev Lett, 1995,74:4091—4094
[15] Sleane A. The ion trap quantum information processor. Appl Phys B, 1997,64: 623
[16] Gershenfield N A, Chuang I L. Bulk spin-resonance quantum computation, Science,1997,275:350.
[17] Cory D G, Fahmy A F, Havel T F. Ensemble quantum computing by NMR spectroscopy. Proc.Nat1.Acad.Sci.USA, 1997,94:1634
[18] Jones J A, Mosca M, Hansen R H. Implementation of a quantum search algorithm on a quantum computer. Nature, 1998,393:344—346
[19] DiVicenzo D P, Bacon D, Kempe J, et a1.Universal quantum computation with the exchange interaction. Nature, 2000,408:339
[20] Kikkawa J M, Smorchkova I P, Samarth N, et a1.Room temperature spin memory in two-dimensional electron Gases. Science, 1997,277:1284
[21] Imamoglu A, Awschalom D D, Burkard G, et a1. Quantum information processing using quantum dot spins andcavity QED. Phys Rev Lett, 1999,83:4204-4207
[22] M Brune, P Nussenzveig, F Schmidt-Kaler, et al. From Lamb shift to light shifts:vacuum and subphoton cavity fields measured by atomic phasesensitive detection. Phys Rev Lett, 1994,72:3339-3342
[23] Turchette Q A, Hood C J, Lange W, et a1.Measurement of conditional phase shifts for quantum logic. Phys Rev Lett, 1995,75:4710—4713
[24] S. Haroche, M. Brune, J.M. Raimond. Manipulation of optical fields by atomic interferometry:quantum variations on a theme by Young. Appl Phys B, 1992,54:355
[25] M Brune, F S Kaler, A Maali, et al. Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity. Phys Rev Lett, 1996,76:1800
[26] E. T. Jaynes, F. W. Cummings. Comparision of quantum and semiclassical radiation theories with application to the beam maser. Proc IEEE, 1963,51:89
[27] H Rauch, A Zeilinger, G Badurek, et al. Comment on Neutron Interferometric Observation of Noncyclic Phase, Phys Lett A, 1975,54:425
[28] E Solano, G S Agarwal, and H Walther. Strong-driving-assisted multipartite entanglement in cavity QED. Phys Rev Lett, 2003,90:027903
[29] 曹卓良. 量子信息中的腔QED技术.量子电子学报,2004,21(2): 243-256
[30] Guo G P, Li C F, Li J, et al. Scheme for the preparation of multiparticle entanglement in cavity QED. Phys Rev A , 2002,65: 042102
[31] M V Berry. Quantal phase factors accompanying adiabatic changes. Proc R Soc London, 1984,392: 45
[32] P W Shor. Scheme for reducing decoherence in quantum computer memory. Phys Rev A, 1995,52:2493
[33] A M Steane. Error Correcting Codes in Quantum Theory. Phys Rev Lett, 1996,77:793
[34] A M Steane. Overhead and noise threshold of fault-tolerant quantum error correction. Phys Rev A, 2003,68:042322
[35] P Zanardi, M Rasetti. Noiseless quantum codes. Phys Rev Lett, 1997,79:3306
[36] P Zanardi, M Rasetti. Quantum computation based on non-abelian phases. Phys Lett A, 1999,264:94
[37] J Pachos, P Zanardi, and M Rasetti. Non-Abelian Berry connections for quantum computation. Phys Rev A, 2000,61(R):010305
[38] J Pachos, H Walther. Quantum computation with trapped ions in an optical cavity. Phys Rev Lett, 2002,89:187903
[39] G Falci, R Fazio, G M Palma, et al. Detection of geometric phases in superconducting nanocircuits. Nature, 2000,407:355
[40] L M Duan, J I Cirac, P Zoller. Geometric manipulation of trapped ions for quantum Computation. Science, 2001,292:1695-1697
[41] J A Jones, V Vedral, A Ekert, et al. A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field. Nature, 1999,403:869
[42] J J Garcia-Ripoll, J I Cirac. Quantum Computation with Unknown Parameters. Phys Rev Lett, 2003,90:127902
[43] X B Wang and M Keiji. Non-adiabatic conditional geometric phase shift with NMR. Phys Rev Lett, 2001,87:097901
[44] S L Zhu, Z D Wang. Unconventional geometric quantum computation. Phys Rev Lett, 2003,91:187902
[45] S B Zheng. Unconventional geometric quantum phase gates with a cavity QED system. Phys Rev A, 2004,70:052320
[46] Y Aharonov and J Anandan. Phase Change during a Cyclic Quantum Evolution. Phys Rev Lett, 1987,58:1593
[47] J Samuel, R Bhandari. General Setting for Berry's Phase. Phys Rev Lett, 1988,60:2339
[48] S L Zhu, Z D Wang, and Y D Zhang. Nonadiabatic noncyclic geometric phase of a spin-1 / 2 particle subject to an arbitrary magnetic field. Phys Rev B, 2000,61:1142
[49] S L Zhu and Z D Wang. Nonadiabatic Monocyclic Geometric Phase and EnsembleAverage Spectrum of Conductance in Disordered Mesoscopic Rings with Spin-Orbit Coupling. Phys Rev Lett, 2000,85:1076
[50] D Leibfried, B De Marco, V Meyer, et al. Experimental demonstration of a robust high-fidelity geometric two ionqubit phase gate. Nature, 2003,422:412
[51] A Luis. Geometric phase in a flat space for electromagnetic scalar waves. J Phys A, 2001,34:7677
[52] X Wang and P Zanardi. Multipartite entangled coherent states. Phys Rev A, 2002,65:032327
[53] C Y Chen, X L Zhang, Z J Deng, et al. Influence from cavity decay on geometric quantum computation in the large-detuning cavity QED model. Phys Rev A, 2006,74:032328
[54] X L Feng, Z Wang, C Wu, et al. Scheme for unconventional geometric quantum computation in cavity QED. Phys Rev A, 2007,75:052312
[55] C Y Chen, M Feng, X L Zhang, et al. Strong-driving-assisted unconventional geometric logic gate in cavity QED. Phys Rev A, 2006,73:032344
[56] X L Feng, Z S Wang, C F Wu, et al. Scheme for unconventional geometric quantum computation in cavity QED. Phys Rev A, 2007,75:052312
[57] S B Zheng. Quantum Logic Gates for Hot Ions without a Speed Limitation. Phys Rev Lett, 2006,90:217901
[58] M Hennrich, T Legero, A Kuhn, et al. Vacuum-Stimulated Raman Scattering Based on Adiabatic Passage in a High-Finesse Optical Cavity. Phys Rev Lett, 2000,85:4872
[59] J K Pachos and A Beige. Decoherence-free dynamical and geometrical entangling phase gates. Phys Rev A, 2004,69:0338l7
[60] P Solinas, P Zanardi, N Zanghi, et al. Semiconductor-based geometrical quantum gates. Phys Rev B, 2003,67:121307
[61] A Rauschenbeutel, G Nogues, S Osnaghi, et al. Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED. Phys Rev Lett, 1999,83:5166