基于无消相干子空间的量子信息过程物理实现研究
|
摘要
量子信息学是一门信息理论和量子理论交叉的新兴学科,它在信道容量、安全和运算速度等许多方面显示出了比经典信息所无法比拟的优势,这些优势归根结底来源于其相干性。然而,现有的量子系统由于其或多或少与环境相互作用导致消相干,从而影响量子信息的处理过程,最终有可能导致信息的丧失。如何克服系统的消相干已经成为许多科学家共同关注的目标。迄今为止,人们提出的解决方案主要有三种：一是量子信息编码；二是通过动力学解耦(dynamical decoupling)的方法；三是拓扑量子计算的方案。其中量子编码的方案由于其适用范围的普遍性而受到广泛关注。量子信息编码主要通过量子纠错和量子避错两种方法来保护量子纠缠态不受环境噪声的影响。前者适用于任意的量子系统的纠错但是需要引入大量的辅助位,后者量子避错的方法由于利用了系统的对称性,因而在处理集体消相干噪声的情形时成为一种十分有效的方案。该方案最先由中国科学技术大学段路明和郭光灿提出,他们用两个原子形成一个原子对作为一个逻辑比特,该逻辑比特构成一个对于集体相位噪声不变的无消相干子空间(Decoherence-free subspace—DFS),在此子空间中进行量子信息处理能够有效的避免消相干。本文主要针对该量子避错方案,提出在此无消相干子空间中基于腔量子电动力学(QED)的物理体系来实现量子信息处理的物理方案,取得的主要成果如下：
(1)基于腔QED系统提出了如何在无消相干空间中实现量子SWAP门。本方案建立在单边泄漏腔的输入输出方程基础上,利用原子作为存储比特,光子作为飞行比特,当一个单光子脉冲和一个囚禁原子的高品质因子腔相互作用时,可以实现两原子的量子相位门,单逻辑比特的Hadamard门和两逻辑比特的量子相位门,在此基础上,我们提出了如何实现一个逻辑比特和一个飞行比特间的量子信息SWAP门方案。此方案不受原子退相位噪声的影响,且光子的损失只影响实验的成功率,不影响保真度。
(2)基于腔QED系统提出了如何在无消相干空间中实现量子密集编码。用腔QED系统实现量子信息的一个主要障碍是腔场的消相干,然而,在这个方案中,通过采用逻辑比特来对量子信息进行编码,消相干被有效的克服。此方案建立在单边泄漏腔的输入输出方程基础上,当通信一方对逻辑比特进行操作时,另一方可以利用逻辑比特的各种门操作来识别,从而达到了通过量子通道来传递经典信息,并且信道容量增大的目的。
Quantum information is a new subject, which is the combination of quantum theory and information theory. Compared with classical information science, it manifests distinct advantages in many respects. For example, information capacity, information security, operates speed, and so on. These advantages are due to the coherence of quantum system. However, decoherence induced from the more or less interaction between quantum system and environment, which will interfere the quantum information processing, even spoil the quantum information. How to resist decoherence has become the aim of many physicist. There are three schemes have been proposed so far, The first is quantum information coded, the second is dynamically decoupled from the environment, and the third is topological quantum computation. In these schemes, quantum information coded has attracted widespread attention for its universal application, which prevents the quantum entanglement from noise mainly through two methods, one is error correction coded, and the other is error protection coded. The former is applicable to any quantum system, but need to introduce a large number of auxiliary bits. The latter, for its symmetry, become a very effective scheme in dealing with collective dephasing. The scheme is proposed by Duan Lu-ming and Guo Guang-can from University of Science and Technology, they use an atom pair consist of two atoms as a logic qubit, which forms a Decoherence-free subspace immune to collective dephasing. The quantum information processing can effectively resist decoherence in the Decoherence-free subspace. The paper proposes some schemes for Physical Implementation of Quantum Information Processing in Decoherence-free Subspace based on cavity quantum electrodynamics.
Our main results include:
(1)We propose a scheme of how to realize quantum SWAP gate in decoherence-free subspace based on cavity QED system. The scheme is built on the input-output formulation of a single-sided cavity, where atom is used as storage qubit and photon is used as flying qubit. We can implement the controlled phase gate between two atoms, the Hadamard gate of one logic qubit and the controlled phase gate between two logic qubits by means of cavity assisted interactions with single-photon pulse. Here we propose a scheme of how to realize the SWAP gate between one logic qubit and one flying qubit. The scheme is immune to dephasing and the loss of photon only affects the successful probability but has no influence on the fidelity.
(2) We propose a scheme of how to implement quantum dense coding in decoherence-free subspace based on cavity QED system. One of the main obstacles for the implementation of quantum information in cavity QED is the decoherence of the cavity field. However, In our scheme, by using logic qubit to encode quantum information, the decoherence can be effectively resisted. The scheme is built on the input-output formulation of a single-sided cavity, when one party operates on the logic qubit, the other party can identify it with the help of the quantum logic qubit gate. So we can transfer the classical information by quantum channel, and information capacity increases.
(1)基于腔QED系统提出了如何在无消相干空间中实现量子SWAP门。本方案建立在单边泄漏腔的输入输出方程基础上,利用原子作为存储比特,光子作为飞行比特,当一个单光子脉冲和一个囚禁原子的高品质因子腔相互作用时,可以实现两原子的量子相位门,单逻辑比特的Hadamard门和两逻辑比特的量子相位门,在此基础上,我们提出了如何实现一个逻辑比特和一个飞行比特间的量子信息SWAP门方案。此方案不受原子退相位噪声的影响,且光子的损失只影响实验的成功率,不影响保真度。
(2)基于腔QED系统提出了如何在无消相干空间中实现量子密集编码。用腔QED系统实现量子信息的一个主要障碍是腔场的消相干,然而,在这个方案中,通过采用逻辑比特来对量子信息进行编码,消相干被有效的克服。此方案建立在单边泄漏腔的输入输出方程基础上,当通信一方对逻辑比特进行操作时,另一方可以利用逻辑比特的各种门操作来识别,从而达到了通过量子通道来传递经典信息,并且信道容量增大的目的。
Quantum information is a new subject, which is the combination of quantum theory and information theory. Compared with classical information science, it manifests distinct advantages in many respects. For example, information capacity, information security, operates speed, and so on. These advantages are due to the coherence of quantum system. However, decoherence induced from the more or less interaction between quantum system and environment, which will interfere the quantum information processing, even spoil the quantum information. How to resist decoherence has become the aim of many physicist. There are three schemes have been proposed so far, The first is quantum information coded, the second is dynamically decoupled from the environment, and the third is topological quantum computation. In these schemes, quantum information coded has attracted widespread attention for its universal application, which prevents the quantum entanglement from noise mainly through two methods, one is error correction coded, and the other is error protection coded. The former is applicable to any quantum system, but need to introduce a large number of auxiliary bits. The latter, for its symmetry, become a very effective scheme in dealing with collective dephasing. The scheme is proposed by Duan Lu-ming and Guo Guang-can from University of Science and Technology, they use an atom pair consist of two atoms as a logic qubit, which forms a Decoherence-free subspace immune to collective dephasing. The quantum information processing can effectively resist decoherence in the Decoherence-free subspace. The paper proposes some schemes for Physical Implementation of Quantum Information Processing in Decoherence-free Subspace based on cavity quantum electrodynamics.
Our main results include:
(1)We propose a scheme of how to realize quantum SWAP gate in decoherence-free subspace based on cavity QED system. The scheme is built on the input-output formulation of a single-sided cavity, where atom is used as storage qubit and photon is used as flying qubit. We can implement the controlled phase gate between two atoms, the Hadamard gate of one logic qubit and the controlled phase gate between two logic qubits by means of cavity assisted interactions with single-photon pulse. Here we propose a scheme of how to realize the SWAP gate between one logic qubit and one flying qubit. The scheme is immune to dephasing and the loss of photon only affects the successful probability but has no influence on the fidelity.
(2) We propose a scheme of how to implement quantum dense coding in decoherence-free subspace based on cavity QED system. One of the main obstacles for the implementation of quantum information in cavity QED is the decoherence of the cavity field. However, In our scheme, by using logic qubit to encode quantum information, the decoherence can be effectively resisted. The scheme is built on the input-output formulation of a single-sided cavity, when one party operates on the logic qubit, the other party can identify it with the help of the quantum logic qubit gate. So we can transfer the classical information by quantum channel, and information capacity increases.
引文
[1]C. A. Ryan, M. Laforest, J. C. Boileau, and R. Laflamme. Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor[J]. Phys. Rev. A 72,062317 (2005).
[2]C. A. Ryan, J. Emerson, D. Poulin, C. Negrevergne, and R. Laflamme. Characterization of Complex Quantum Dynamics with a Scalable NMR Information Processor[J]. Phys. Rev. Lett.95,250502 (2005).
[3]Tycho Sleator and Harald Weinfurter. Realizable Universal Quantum Logic Gates[J]. Phys. Rev. Lett.74,4087 (1995).
[4]Shi-Biao Zheng. One-Step Synthesis of Multiatom Greenberger-Horne-Zeilinger States[J]. Phys. Rev. Lett.87,230404 (2001).
[5]J. I. Cirac and P. Zoller. Quantum Computations with Cold Trapped Ions[J]. Phys. Rev. Lett.74,4091 (1995).
[6]A. Steane. The ion trap quantum information processor [J]. Appl. Phys. B-lasers.64,623 (1997).
[7]E. Knill, R. Laflamme, G. J. Milburn. A scheme for efficient quantum computation with linear optics[J]. Nature 409,46 (2001).
[8]John C. Howell and John A. Yeazell. Quantum Computation through Entangling Single Photons in Multipath Interferometers [J]. Phys. Rev. Lett.85,198 (2000).
[9]G. P. Berman, G. D. Doolen, P. C. Hamme, and V. I. Tsifrinovich. Magnetic Resonance Force Microscopy Quantum Computer with Tellurium Donors in Silicon[J]. Phys. Rev. Lett.86,2894 (2001).
[10]C. H. W. Barnes, J. M. Shilton, and A. M. Robinson. Quantum computation using electrons trapped by surface acoustic waves[J]. Phys. Rev. B 62,8410 (2000).
[11]B. E. Kane. A silicon-based nuclear spin quantum computer [J]. Nature 393,133 (1998).
[12]F. Bodoky and M. Blaauboer. Production of multipartite entanglement for electron spins in quantum dots [J]. Phys. Rev. A 76,052309 (2007).
[13]Fabrizio Buscemi, Paolo Bordone, and Andrea Bertoni. Carrier-carrier entanglement and transport resonances in semiconductor quantum dots[J]. Phys. Rev. B 76,195317 (2007).
[14]P. M. Platzman and M. I. Dykman. Quantum Computing with Electrons Floating on Liquid Helium[J]. Science 284,1967 (1999).
[15]Yuriy Makhlin, Gerd Scohn, Alexander Shnirman. Josephson-junction qubits with controlled couplings[J]. Nature 398,305 (1999).
[16]Yuriy Makhlin. Quantum-state engineering with Josephson-junction devices[J]. Rev. Mod. Phys.73,357 (2001).
[17]Lu-Ming Duan and Guang-Can Guo. Preserving Coherence in Quantum Computation by Pairing Quantum Bits[J]. Phys. Rev. Lett.79,1953 (1997).
[18]Lu-Ming Duan and Guang-Can Guo. Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment[J]. Phys. Rev. A 57,737 (1998).
[19]P. Zanardi and M. Rasetti. Noiseless Quantum Codes[J]. Phys. Rev. Lett.79,3306 (1997).
[20]D. A. Lidar, I. L. Chuang, and K. B. Whaley. Decoherence-Free Subspaces for Quantum Computation[J]. Phys. Rev. Lett.81,2594 (1998).
[21]D. A. Lidar, D. Bacon, and K. B. Whaley. Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes[J]. Phys. Rev. Lett.82,4556 (1999).
[22]Paul G. Kwiat, Andrew J. Berglund, Joseph B. Altepeter, and Andrew G. White. Experimental Verification of Decoherence-Free Subspaces [J]. Science 290,498 (2000).
[23]D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. A Decoherence-Free Quantum Memory Using Trapped Ions[J]. Science 291,1013 (2001).
[24]Lorenza Viola, Evan M. Fortunato, Marco A. Pravia, Emanuel Knill, Raymond Laflamme, and David G. Cory. Experimental Realization of Noiseless Subsystems for Quantum Information Processing[J]. Science 293,2059 (2001).
[25]Almut Beige, Danie Braun and Peter L Knight. Driving atoms into decoherence-free states[J]. New J Phys.2,22 (2000).
[26]Ben Tregenna, Almut Beige, and Peter L. Knight. Quantum computing in a macroscopic dark period[J]. Phys. Rev. A 65,032305 (2002).
[27]A. Beige, D. Braun, B. Tregennan, P. L. Knight, Quantum computing using dissipation to remain in a decoherence-free subspace[J]. Phys. Rev. Lett.85,1762 (2000).
[28]Jiannis K. Pachos and Almut Beige. Decoherence-free dynamical and geometrical entangling phase gates[J]. Phys. Rev. A 69,033817 (2004).
[29]A. Lamas-Linares, J. C. Howell, D. Bouwmeester. Stimulated emission of polarization-entangled photons[J]. Nature 412,887 (2001).
[30]J.-W. Pan, C. Simon, C. Brukner, A. Zeilinger. Entanglement purification for quantum communication [J]. Nature 410,1067 (2001).
[31]Charles H. Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A. Smolin and William K. Wootters[J]. Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J]. Phys. Rev. Lett.76,722 (1996).
[32]Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, Anton Zeilinger. Experimental quantum teleportation [J]. Nature 390,575 (1997).
[33]Jian-Wei Pan, Sara Gasparoni, Markus Aspelmeyer, Thomas Jennewein, Anton Zeilinger. Experimental realization of freely propagating teleported qubits[J]. Nature 421,721 (2003).
[34]Zhi Zhao, An-Ning Zhang, Yu-Ao Chenl, Han Zhang, Jiang-Feng Du, Tao Yang, and Jian-Wei Pan. Experimental Demonstration of a Nondestructive Controlled-NOT Quantum Gate for Two Independent Photon Qubits[J]. Phys. Rev. Lett.94,030501 (2005).
[35]Sara Gasparoni, Jian-Wei Pan, Philip Walther, Terry Rudolph, and Anton Zeilinger. Realization of a Photonic Controlled-NOT Gate Sufficient for Quantum Computation[J]. Phys. Rev. Lett.93,020504 (2004).
[36]Y. Luo and K. T. Chan, Quantum cryptography with entangled multiphotons of the same polarization, Phys. Rev. A 70,042302 (2004).
[37]赵千川[译],量子计算和量子信息[M].北京：清华大学出版社,2004.
[38]李承祖,量子通信和量子计算[M].长沙：国防科大出版社,2000.
[39]Charles H. Bennett, Gilles Brassard, Claude Crepeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev. Lett.70,1895 (1993).
[40]L. K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of Computation[R].212-214 (1996).
[41]L. K.Grover. Quantum Mechanics Helps in Searching for a Needle in a Haystack[J]. Phys. Rev. Lett.79,325-328 (1997).
[42]J. A. Jones, M. Mosca, and R. H. Hansen. Implementation of a quantum search algorithm on a quantum computer [J]. Nature.393,344 (1998).
[43]I. L. Chuang, N.Gershenfeld and M. Kubinec. Experimental Implementation of Fast Quantum Searching [J]. Phys. Rev. Lett.80, 3408 (1998).
[44]P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger. Experimental one-way quantum computing [J]. Nature.434,169 (2005).
[45]M. Riebe, H. Haffner, C. F. Roos, W. Hansel, J. Benhelm, G. P. T. Lancaster, T. W. Korber, C. Becher, F. Schmidt-Kaler, D. F. V. James, et al. Deterministic quantum teleportation with atoms [J]. Nature. 429,734 (2004).
[46]K. A. Brickman, P. C. Hal jan, et al.. Implementation of Grover's quantum search algorithm in a scalable system [J], Phy. Rev. A.72, 050306(R) (2005).
[47]. Chiaverini, J. Britton, D. Leibfried, E. Knill, M. D. Barrett, R. B. Blakestad, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, T. Schaetz, and D. J. Wineland. Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System [J]. Science.308,997 (2005).
[48]M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, et al. Deterministic quantum teleportation of atomic qubits [J]. Nature.429, 737 (2005).
[49]J. M. Raimond, M. Brune, and S. Haroche. Manipulating quantum entanglement with atoms and photons in a cavity[J]. Rev. Mod. Phys. 73,565 (2001).
[50]J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nagerl, D. M. Stamper-Kurn, and H. J. Kimble. State-Insensitive Cooling and Trapping of Single Atoms in an Optical Cavity[J]. Phys. Rev. Lett. 90,133602 (2003).
[51]S. Haroche, J. M. Raimond. In Cavity Quantum Electrodynamics [M]. Academic Press.123 (1994).
[52]Kerry J. Vahala. Optical microcavities[J]. Nature 424,839 (2003).
[53]X. D. Fan, M. C. Lonergan et al.. Enhanced spontaneous emission from semiconductor nanocrystals embedded in whispering gallery optical microcavities [J]. Phys. Rev. B 64,115310 (2001).
[54]0. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim. Two-Dimensional Photonic Band-Gap Defect Mode Laser[J]. Science 284,1819 (1999).
[55]Jelena Vuckovic, Marko Loncar, Hideo Mabuchi, and Axel Scherer. Design of photonic crystal microcavities for cavity QED[J]. Phys. Rev. E 65,016608 (2001).
[56]0. Painter, R. K. Lee, A. Scherer et al.. Two-Dimensional Photonic Band-Gap Defect Mode Laser[J]. Science 284,1819 (1999).
[57]G. J. Steven, S. Fan, A. Mekis et al.. Multipole-cancellation mechanism for hight-Q cavities in the absence of a complete photonic band gap [J]. Appl. Phys. Lett.78,3388 (2001).
[58]D. F. Walls and G. J. Milburn. Quantum Optics[M]. Springer-Verlag (1994).
[59]林秀敏.基于腔QED的量子信息处理[D].中国科学技术大学(2005).
[60]W. Gardiner and P. Zoller. Quantum Noise[M]. Springer-Verlag (1991).
[61]M. J. Collett and C. W. Gardiner. Squeezing of intracavity and traveling-wave light fields produced in parametric amplification[J]. Phys. Rev. A 30,1386 (1984).
[62]C. W. Gardiner and M. J. Collett. Input and output in damped quantum systems:Quantum stochastic differential equations and the master equation[J]. Phys. Rev. A 31,3761 (1985).
[63]A. M. Steane. Error Correcting Codes in Quantum Theory[J]. Phys. Rev. Lett.77,793 (1996).
[64]Lorenza Violal, Emanuel Knill, and Seth Lloyd. Dynamical Decoupling of Open Quantum Systems[J]. Phys. Rev. Lett.82,2417 (1999).
[65]H. Bombin. Topological subsystem codes[J]. Phys. Rev. A 81,032101 (2010).
[66]Paul G. Kwiat, Andrew J. Berglund, Joseph B. Altepeter, and Andrew G. White. Experimental Verification of Decoherence-Free Subspaces[J]. Science.290,498 (2000).
[67]D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. A Decoherence-Free Quantum Memory Using Trapped Ions[J]. Science 291,1013 (2001).
[68]L.-M. Duan and H. J. Kimble. Scalable Photonic Quantum Computation through Cavity-Assisted Interactions [J]. Phys. Rev. Lett.92,127902 (2004).
[69]L.-M. Duan, B. Wang, and H. J. Kimble. Robust quantum gates on neutral atoms with cavity-assisted photon scattering[J]. Phys. Rev. A 72,032333 (2005).
[70]J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, H. J. Kimble. Experimental realization of a one-atom laser in the regime of strong coupling[J]. Nature 425,268 (2003).
[71]C. K. Law and J. H. Eberly. Synthesis of arbitrary superposition of Zeeman states in an atom[J]. Opt. Express 2,368 (1998).
[72]Hua Wei, Zhijiao Deng, XiaoLong Zhang, and Mang Feng. Transfer and teleportation of quantum states encoded in decoherence-free subspace[J]. Phys. Rev. A 76,054304 (2007).
[73]Hua wei, Ranran Fang, Ji-Bing Liu, Fei Zhou, Wan-Li Yang and Zhi-Jiao Deng. Two-qubit Grover search in a dephasing-free subspace in cavity QED. J. Phys. B:At. Mol. Opt. Phys. 41,085506 (2008).
[74]Lin-mei Liang and Cheng-zu Li. Realization of quantum SWAP gate between flying and stationary qubits[J]. Phys. Rev. A 72,024303 (2005).
[75]Yun-Feng Xiao, Xiu-Min Lin, Jie Gao, Yong Yang, Zheng-Fu Han, and Guang-Can Guo. Realizing quantum controlled phase flip through cavity QED[J]. Phys. Rev. A 70,042314 (2004).
[76]Peng Xue and Yun-Feng Xiao. Universal Quantum Computation in Decoherence-Free Subspace with Neutral Atoms [J]. Phys. Rev. Lett.97, 140501 (2006).
[77]Pan Guo-Zhu, Yang Ming and Cao Zhuo-Liang. Quantum superdense coding via cavity-assisted interactions[J]. Chinese Physics B 18,2319 (2009).
[78]Hua Wei, Wan Li Yang, Zhi Jiao Deng and Mang Feng. Many-qubit network employing cavity QED in a decoherence-free subspace[J]. Phys. Rev. A 78,014304 (2008).
[79]Z. J. Deng, M. Feng, and K. L. Gao. Preparation of entangled states of four remote atomic qubits in decoherence-free subspace[J]. Phys. Rev. A 75,024302 (2007).
[80]Kaoru Shimizu, Nobuyuki Imoto and Takaaki Mukai. Dense coding in photonic quantum communication with enhanced information capacity[J]. Phys. Rev. A 59,1092 (1999).
[81]Yu-Bo Sheng, Fu-Guo Deng, and Hong-Yu Zhou. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity[J]. Phys. Rev. A 77,042308 (2008).
[82]Markus Hi jlkema, Bernhard Weber, Holger P. Specht, Simon C. Webster, Axel Kuhn, Gerhard Rempe. A single-photon server with just one atom[J]. Nature Physics 3,253 (2007).
[83]J. A. Sauer, K.M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman. Cavity QED with optically transported atoms[J]. Phys. Rev. A 69,051804(R) (2004).
[84]A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt. Coupling a Single Atomic Quantum Bit to a High Finesse Optical Cavity[J]. Phys. Rev. Lett.89,103001 (2002).
[2]C. A. Ryan, J. Emerson, D. Poulin, C. Negrevergne, and R. Laflamme. Characterization of Complex Quantum Dynamics with a Scalable NMR Information Processor[J]. Phys. Rev. Lett.95,250502 (2005).
[3]Tycho Sleator and Harald Weinfurter. Realizable Universal Quantum Logic Gates[J]. Phys. Rev. Lett.74,4087 (1995).
[4]Shi-Biao Zheng. One-Step Synthesis of Multiatom Greenberger-Horne-Zeilinger States[J]. Phys. Rev. Lett.87,230404 (2001).
[5]J. I. Cirac and P. Zoller. Quantum Computations with Cold Trapped Ions[J]. Phys. Rev. Lett.74,4091 (1995).
[6]A. Steane. The ion trap quantum information processor [J]. Appl. Phys. B-lasers.64,623 (1997).
[7]E. Knill, R. Laflamme, G. J. Milburn. A scheme for efficient quantum computation with linear optics[J]. Nature 409,46 (2001).
[8]John C. Howell and John A. Yeazell. Quantum Computation through Entangling Single Photons in Multipath Interferometers [J]. Phys. Rev. Lett.85,198 (2000).
[9]G. P. Berman, G. D. Doolen, P. C. Hamme, and V. I. Tsifrinovich. Magnetic Resonance Force Microscopy Quantum Computer with Tellurium Donors in Silicon[J]. Phys. Rev. Lett.86,2894 (2001).
[10]C. H. W. Barnes, J. M. Shilton, and A. M. Robinson. Quantum computation using electrons trapped by surface acoustic waves[J]. Phys. Rev. B 62,8410 (2000).
[11]B. E. Kane. A silicon-based nuclear spin quantum computer [J]. Nature 393,133 (1998).
[12]F. Bodoky and M. Blaauboer. Production of multipartite entanglement for electron spins in quantum dots [J]. Phys. Rev. A 76,052309 (2007).
[13]Fabrizio Buscemi, Paolo Bordone, and Andrea Bertoni. Carrier-carrier entanglement and transport resonances in semiconductor quantum dots[J]. Phys. Rev. B 76,195317 (2007).
[14]P. M. Platzman and M. I. Dykman. Quantum Computing with Electrons Floating on Liquid Helium[J]. Science 284,1967 (1999).
[15]Yuriy Makhlin, Gerd Scohn, Alexander Shnirman. Josephson-junction qubits with controlled couplings[J]. Nature 398,305 (1999).
[16]Yuriy Makhlin. Quantum-state engineering with Josephson-junction devices[J]. Rev. Mod. Phys.73,357 (2001).
[17]Lu-Ming Duan and Guang-Can Guo. Preserving Coherence in Quantum Computation by Pairing Quantum Bits[J]. Phys. Rev. Lett.79,1953 (1997).
[18]Lu-Ming Duan and Guang-Can Guo. Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment[J]. Phys. Rev. A 57,737 (1998).
[19]P. Zanardi and M. Rasetti. Noiseless Quantum Codes[J]. Phys. Rev. Lett.79,3306 (1997).
[20]D. A. Lidar, I. L. Chuang, and K. B. Whaley. Decoherence-Free Subspaces for Quantum Computation[J]. Phys. Rev. Lett.81,2594 (1998).
[21]D. A. Lidar, D. Bacon, and K. B. Whaley. Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes[J]. Phys. Rev. Lett.82,4556 (1999).
[22]Paul G. Kwiat, Andrew J. Berglund, Joseph B. Altepeter, and Andrew G. White. Experimental Verification of Decoherence-Free Subspaces [J]. Science 290,498 (2000).
[23]D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. A Decoherence-Free Quantum Memory Using Trapped Ions[J]. Science 291,1013 (2001).
[24]Lorenza Viola, Evan M. Fortunato, Marco A. Pravia, Emanuel Knill, Raymond Laflamme, and David G. Cory. Experimental Realization of Noiseless Subsystems for Quantum Information Processing[J]. Science 293,2059 (2001).
[25]Almut Beige, Danie Braun and Peter L Knight. Driving atoms into decoherence-free states[J]. New J Phys.2,22 (2000).
[26]Ben Tregenna, Almut Beige, and Peter L. Knight. Quantum computing in a macroscopic dark period[J]. Phys. Rev. A 65,032305 (2002).
[27]A. Beige, D. Braun, B. Tregennan, P. L. Knight, Quantum computing using dissipation to remain in a decoherence-free subspace[J]. Phys. Rev. Lett.85,1762 (2000).
[28]Jiannis K. Pachos and Almut Beige. Decoherence-free dynamical and geometrical entangling phase gates[J]. Phys. Rev. A 69,033817 (2004).
[29]A. Lamas-Linares, J. C. Howell, D. Bouwmeester. Stimulated emission of polarization-entangled photons[J]. Nature 412,887 (2001).
[30]J.-W. Pan, C. Simon, C. Brukner, A. Zeilinger. Entanglement purification for quantum communication [J]. Nature 410,1067 (2001).
[31]Charles H. Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A. Smolin and William K. Wootters[J]. Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J]. Phys. Rev. Lett.76,722 (1996).
[32]Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, Anton Zeilinger. Experimental quantum teleportation [J]. Nature 390,575 (1997).
[33]Jian-Wei Pan, Sara Gasparoni, Markus Aspelmeyer, Thomas Jennewein, Anton Zeilinger. Experimental realization of freely propagating teleported qubits[J]. Nature 421,721 (2003).
[34]Zhi Zhao, An-Ning Zhang, Yu-Ao Chenl, Han Zhang, Jiang-Feng Du, Tao Yang, and Jian-Wei Pan. Experimental Demonstration of a Nondestructive Controlled-NOT Quantum Gate for Two Independent Photon Qubits[J]. Phys. Rev. Lett.94,030501 (2005).
[35]Sara Gasparoni, Jian-Wei Pan, Philip Walther, Terry Rudolph, and Anton Zeilinger. Realization of a Photonic Controlled-NOT Gate Sufficient for Quantum Computation[J]. Phys. Rev. Lett.93,020504 (2004).
[36]Y. Luo and K. T. Chan, Quantum cryptography with entangled multiphotons of the same polarization, Phys. Rev. A 70,042302 (2004).
[37]赵千川[译],量子计算和量子信息[M].北京：清华大学出版社,2004.
[38]李承祖,量子通信和量子计算[M].长沙：国防科大出版社,2000.
[39]Charles H. Bennett, Gilles Brassard, Claude Crepeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev. Lett.70,1895 (1993).
[40]L. K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of Computation[R].212-214 (1996).
[41]L. K.Grover. Quantum Mechanics Helps in Searching for a Needle in a Haystack[J]. Phys. Rev. Lett.79,325-328 (1997).
[42]J. A. Jones, M. Mosca, and R. H. Hansen. Implementation of a quantum search algorithm on a quantum computer [J]. Nature.393,344 (1998).
[43]I. L. Chuang, N.Gershenfeld and M. Kubinec. Experimental Implementation of Fast Quantum Searching [J]. Phys. Rev. Lett.80, 3408 (1998).
[44]P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger. Experimental one-way quantum computing [J]. Nature.434,169 (2005).
[45]M. Riebe, H. Haffner, C. F. Roos, W. Hansel, J. Benhelm, G. P. T. Lancaster, T. W. Korber, C. Becher, F. Schmidt-Kaler, D. F. V. James, et al. Deterministic quantum teleportation with atoms [J]. Nature. 429,734 (2004).
[46]K. A. Brickman, P. C. Hal jan, et al.. Implementation of Grover's quantum search algorithm in a scalable system [J], Phy. Rev. A.72, 050306(R) (2005).
[47]. Chiaverini, J. Britton, D. Leibfried, E. Knill, M. D. Barrett, R. B. Blakestad, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, T. Schaetz, and D. J. Wineland. Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System [J]. Science.308,997 (2005).
[48]M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, et al. Deterministic quantum teleportation of atomic qubits [J]. Nature.429, 737 (2005).
[49]J. M. Raimond, M. Brune, and S. Haroche. Manipulating quantum entanglement with atoms and photons in a cavity[J]. Rev. Mod. Phys. 73,565 (2001).
[50]J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nagerl, D. M. Stamper-Kurn, and H. J. Kimble. State-Insensitive Cooling and Trapping of Single Atoms in an Optical Cavity[J]. Phys. Rev. Lett. 90,133602 (2003).
[51]S. Haroche, J. M. Raimond. In Cavity Quantum Electrodynamics [M]. Academic Press.123 (1994).
[52]Kerry J. Vahala. Optical microcavities[J]. Nature 424,839 (2003).
[53]X. D. Fan, M. C. Lonergan et al.. Enhanced spontaneous emission from semiconductor nanocrystals embedded in whispering gallery optical microcavities [J]. Phys. Rev. B 64,115310 (2001).
[54]0. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim. Two-Dimensional Photonic Band-Gap Defect Mode Laser[J]. Science 284,1819 (1999).
[55]Jelena Vuckovic, Marko Loncar, Hideo Mabuchi, and Axel Scherer. Design of photonic crystal microcavities for cavity QED[J]. Phys. Rev. E 65,016608 (2001).
[56]0. Painter, R. K. Lee, A. Scherer et al.. Two-Dimensional Photonic Band-Gap Defect Mode Laser[J]. Science 284,1819 (1999).
[57]G. J. Steven, S. Fan, A. Mekis et al.. Multipole-cancellation mechanism for hight-Q cavities in the absence of a complete photonic band gap [J]. Appl. Phys. Lett.78,3388 (2001).
[58]D. F. Walls and G. J. Milburn. Quantum Optics[M]. Springer-Verlag (1994).
[59]林秀敏.基于腔QED的量子信息处理[D].中国科学技术大学(2005).
[60]W. Gardiner and P. Zoller. Quantum Noise[M]. Springer-Verlag (1991).
[61]M. J. Collett and C. W. Gardiner. Squeezing of intracavity and traveling-wave light fields produced in parametric amplification[J]. Phys. Rev. A 30,1386 (1984).
[62]C. W. Gardiner and M. J. Collett. Input and output in damped quantum systems:Quantum stochastic differential equations and the master equation[J]. Phys. Rev. A 31,3761 (1985).
[63]A. M. Steane. Error Correcting Codes in Quantum Theory[J]. Phys. Rev. Lett.77,793 (1996).
[64]Lorenza Violal, Emanuel Knill, and Seth Lloyd. Dynamical Decoupling of Open Quantum Systems[J]. Phys. Rev. Lett.82,2417 (1999).
[65]H. Bombin. Topological subsystem codes[J]. Phys. Rev. A 81,032101 (2010).
[66]Paul G. Kwiat, Andrew J. Berglund, Joseph B. Altepeter, and Andrew G. White. Experimental Verification of Decoherence-Free Subspaces[J]. Science.290,498 (2000).
[67]D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. A Decoherence-Free Quantum Memory Using Trapped Ions[J]. Science 291,1013 (2001).
[68]L.-M. Duan and H. J. Kimble. Scalable Photonic Quantum Computation through Cavity-Assisted Interactions [J]. Phys. Rev. Lett.92,127902 (2004).
[69]L.-M. Duan, B. Wang, and H. J. Kimble. Robust quantum gates on neutral atoms with cavity-assisted photon scattering[J]. Phys. Rev. A 72,032333 (2005).
[70]J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, H. J. Kimble. Experimental realization of a one-atom laser in the regime of strong coupling[J]. Nature 425,268 (2003).
[71]C. K. Law and J. H. Eberly. Synthesis of arbitrary superposition of Zeeman states in an atom[J]. Opt. Express 2,368 (1998).
[72]Hua Wei, Zhijiao Deng, XiaoLong Zhang, and Mang Feng. Transfer and teleportation of quantum states encoded in decoherence-free subspace[J]. Phys. Rev. A 76,054304 (2007).
[73]Hua wei, Ranran Fang, Ji-Bing Liu, Fei Zhou, Wan-Li Yang and Zhi-Jiao Deng. Two-qubit Grover search in a dephasing-free subspace in cavity QED. J. Phys. B:At. Mol. Opt. Phys. 41,085506 (2008).
[74]Lin-mei Liang and Cheng-zu Li. Realization of quantum SWAP gate between flying and stationary qubits[J]. Phys. Rev. A 72,024303 (2005).
[75]Yun-Feng Xiao, Xiu-Min Lin, Jie Gao, Yong Yang, Zheng-Fu Han, and Guang-Can Guo. Realizing quantum controlled phase flip through cavity QED[J]. Phys. Rev. A 70,042314 (2004).
[76]Peng Xue and Yun-Feng Xiao. Universal Quantum Computation in Decoherence-Free Subspace with Neutral Atoms [J]. Phys. Rev. Lett.97, 140501 (2006).
[77]Pan Guo-Zhu, Yang Ming and Cao Zhuo-Liang. Quantum superdense coding via cavity-assisted interactions[J]. Chinese Physics B 18,2319 (2009).
[78]Hua Wei, Wan Li Yang, Zhi Jiao Deng and Mang Feng. Many-qubit network employing cavity QED in a decoherence-free subspace[J]. Phys. Rev. A 78,014304 (2008).
[79]Z. J. Deng, M. Feng, and K. L. Gao. Preparation of entangled states of four remote atomic qubits in decoherence-free subspace[J]. Phys. Rev. A 75,024302 (2007).
[80]Kaoru Shimizu, Nobuyuki Imoto and Takaaki Mukai. Dense coding in photonic quantum communication with enhanced information capacity[J]. Phys. Rev. A 59,1092 (1999).
[81]Yu-Bo Sheng, Fu-Guo Deng, and Hong-Yu Zhou. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity[J]. Phys. Rev. A 77,042308 (2008).
[82]Markus Hi jlkema, Bernhard Weber, Holger P. Specht, Simon C. Webster, Axel Kuhn, Gerhard Rempe. A single-photon server with just one atom[J]. Nature Physics 3,253 (2007).
[83]J. A. Sauer, K.M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman. Cavity QED with optically transported atoms[J]. Phys. Rev. A 69,051804(R) (2004).
[84]A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt. Coupling a Single Atomic Quantum Bit to a High Finesse Optical Cavity[J]. Phys. Rev. Lett.89,103001 (2002).