固态量子比特退相干和消纠缠研究
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摘要
近年来,量子计算己成为量子力学和计算机科学的交叉的活跃学科。由于相干的数据处理能力,使得量子计算受到物理学和信息科学领域中科研人员的热切关注。基于固态量子比特的量子计算因其可集成性和良好的可控性以及读取性能,因而被认为是最有可能实现量子计算机的方案。研究固态量子比特的退相干和纠缠等相关问题,成为了近年来量子计算领域中的热点问题之一。本文主要研究了双量子点电荷量子比特等几种固态量子比特模型的退相干和消纠缠。第一章,我们简要介绍了固态量子比特的几种实现方案。第二章,我们在一般框架内给出了退相干和纠缠理论,并介绍了处理包括退相干和纠缠在内的开放量子系统的问题的量子主方程的方法。在第三章中,我们采用主方程的方法分别研究了双量子点电荷量子比特耦合于环境:压电声子库(PCPB)、变形声子库(DCPB)、欧姆库以及次欧姆库、超欧姆库情况下的退相干的演化情况,验证了当环境为PCPB和DCPB时,量子比特的退相干时间远小于实验结果的观点,并且提出欧姆库可能是引起双量子点电荷量子比特退相干的主要机制。在第四章,通过数值计算方法,我们研究了含时外场控制的开放量子比特的相干性的演化情况,分析了驱动外场的振幅和频率的变化对量子比特退相干的影响,指出量子比特的退相干受到的振幅的影响是比较大的,而且影响是不单调的,相反频率对退相干的影响并不明显。在第五章,我们采用主方程的方法,系统地研究了耦合于独立环境(相同或者不同)以及共同环境的两个相互作用的量子比特的纠缠的演化情况。我们得到了处于不同初态:最大纠缠态、一般纠缠态、直积态的量子比特在不同温度,不同耗散强度下的纠缠动力学,指出环境通常对两体纠缠的破坏作用和在某些条件下的积极作用;以及观察到了纠缠产生,死亡以及在T=0K伴随恒定振幅微小振荡的稳态纠缠的新物理现象,并且指出真空振荡可能是产生该现象的主要原因。最后一章,我们对本文做了总结,并给出几点展望。
Quantum computation is an interdiscipline of Quantum Mechanics and computer science. Recently quantum information processing has attracted much attention due to the potential advantages provided by quantum-mechanical principles such as entanglement and coherence. With the robust macroscopic quantum behavior and scalability, solid-state qubits are widely regarded as excellent candidates due to inherent scalability using well-established microfabrication techniques. So studies on the dynamics of coherence and entanglement for such qubits become one of the most important issues. This dissertation mainly focuses on decoherence and entanglement of some solid-state qubits such as double quantum dots qubits. In chapter 1 and chapter 2, brief reviews about some candidates for qubits and theory about decoherence and entanglement are given respectively. In chapter 3, we investigate decoherence times of a double quantum dot (DQD) charge qubit in different kinds of baths, namely when it is coupled to the piezoelectric coupling phonon bath (PCPB), the deformation coupling phonon bath (DCPB), Ohmic bath, sub-Ohmic bath and supra-Ohmic bath. The dynamics of the qubit are investigated with two forms of master equation respectively. It is found that our results for cases PCPB and DCPB are in the same magnitude with those obtained via the exact path integral methods, while for case Ohmic bath, the decoherence time is in well agreement with the experimental value. In chapter 4, decoherence of a qubit coupled to an environment and driven by an external time-dependent field is investigated by numerically solving the master equation. It is shown that decoherence of the qubit has been significantly affected by the amplitude of the driving field, however, the frequency of the driving field has a little influence on decoherence of the qubit. In chapter 5, we study the influence of the environment on the entanglement of two interacting qubits coupled to a common bath and two independent baths (including the cases that the two independent baths are different and the same). With the system initially prepared in three different states: maximally entangled state, entangled state, separable state, the evolutions of entanglement under various temperatures and damping strengths have been obtained. We found that in most cases, the environment is destructive to the production of entanglement, but can be constructive under certain conditions. At zero temperature, the phenomena of entanglement sudden birth (ESB) and entanglement sudden death (ESD), as well as the presence of a stationary entanglement with constant small amplitude oscillations were observed. In the last chapter, we give some conclusions and some expectations.
Quantum computation is an interdiscipline of Quantum Mechanics and computer science. Recently quantum information processing has attracted much attention due to the potential advantages provided by quantum-mechanical principles such as entanglement and coherence. With the robust macroscopic quantum behavior and scalability, solid-state qubits are widely regarded as excellent candidates due to inherent scalability using well-established microfabrication techniques. So studies on the dynamics of coherence and entanglement for such qubits become one of the most important issues. This dissertation mainly focuses on decoherence and entanglement of some solid-state qubits such as double quantum dots qubits. In chapter 1 and chapter 2, brief reviews about some candidates for qubits and theory about decoherence and entanglement are given respectively. In chapter 3, we investigate decoherence times of a double quantum dot (DQD) charge qubit in different kinds of baths, namely when it is coupled to the piezoelectric coupling phonon bath (PCPB), the deformation coupling phonon bath (DCPB), Ohmic bath, sub-Ohmic bath and supra-Ohmic bath. The dynamics of the qubit are investigated with two forms of master equation respectively. It is found that our results for cases PCPB and DCPB are in the same magnitude with those obtained via the exact path integral methods, while for case Ohmic bath, the decoherence time is in well agreement with the experimental value. In chapter 4, decoherence of a qubit coupled to an environment and driven by an external time-dependent field is investigated by numerically solving the master equation. It is shown that decoherence of the qubit has been significantly affected by the amplitude of the driving field, however, the frequency of the driving field has a little influence on decoherence of the qubit. In chapter 5, we study the influence of the environment on the entanglement of two interacting qubits coupled to a common bath and two independent baths (including the cases that the two independent baths are different and the same). With the system initially prepared in three different states: maximally entangled state, entangled state, separable state, the evolutions of entanglement under various temperatures and damping strengths have been obtained. We found that in most cases, the environment is destructive to the production of entanglement, but can be constructive under certain conditions. At zero temperature, the phenomena of entanglement sudden birth (ESB) and entanglement sudden death (ESD), as well as the presence of a stationary entanglement with constant small amplitude oscillations were observed. In the last chapter, we give some conclusions and some expectations.
引文
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[20] Makhlin Y, Schon G, Shnirman A, Josephon-junction qubits with controlled couplings, Nature, 1999, 398: 305～307.
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[24] Wojciech Hubert Zurek, Decoherence, einselection, and the quantum origins of the clas-sical, Rev. Mod. Phys., 2003, 75: 715～775.
[25] Buchleitner, A., Viviescas, C., Tiersch, M. (Eds.), Entanglement and Decoherence, Lecture Notes in Physics, Springer, 2009.
[26] Luigi Amico, Rosario Fazio, Andreas Osterloh, Vlatko Vedral, Entanglement in many-body systems, Rev. Mod. Phys., 2008, 80: 517～576.
[27] Ryszard Horodecki, Pawel Horodecki, Michal Horodecki, Karol Horodecki, Quantum entanglement, arXiv: quant-ph/0702225.
[28] Lluís Masanes, Yeong-Cherng Liang, Andrew C. Doherty, All Bipartite Entangled Stat-es Display Some Hidden Nonlocality, Phys. Rev. Lett., 2008, 100: 090403～090406.
[29] Samuel L. Braunstein, A. Mann, M. Revzen, Maximal violation of Bell inequalities for mixed states, Phys. Rev. Lett., 1992, 68: 3259～3261.
[30] Marlan O. Scully, M. Suhail Zubairy, Quantum Optics, Cambridge University Press, 1997.
[31] K. Blum, Density Matrix Theory and Applications, 2nd edition, Springer, 1981.
[32] T. Fujisawa, T. H. Oosterkamp, W. G. vander Wiel, B. W. Broer, R. Aguado, S. Tarcc-ha, L. P. Kouwenhoven, Spontaneous emission spectrum in double quantum dot devices, Scien-ce, 1998, 282: 932～935.
[33] T. H. Oosterkamp, T. Fujisawa, W. G. vanderWiel, K. Ishibashi, R. V. Hijman, S. Taru-cha, L. P. Kouwenhoven, Microwave spectroscopy of a quantum-dot molecule, Nature, 1998, 395: 873～876.
[34] S. Gardelis, C. G. Smith, J. Cooper, D. A. Ritchie, E. H. Linfield, Y. Jin, M. Pepper, De-phasing in an isolated double quantum dot system deduced from single-electron polarization m-easurements, Phys. Rev. B, 2003, 67: 073302～073305.
[35] L. C. L. Hollenberg, A. S. Dzurak, C. Wellard, A. R. Hamilton, D. J. Reilly, G. J. Milb-urn, R. G. Clark, Charge based quantum computing using single donors in semiconductors, Phys. Rev. B, 2004, 69: 113301～113304.
[36] T. Brandes, Coherent and collective quantum optical effects in mesoscopic, Phys. Rep., 2005, 408: 315–474.
[37] Z. J. Wu, K. D. Zhu, X. Z. Yuan, Y. W. Jiang, H. Zheng, Charge qubit dynamics in a double quantum dot coupled to phonons, Phys. Rev. B, 2005, 71: 205323～205329.
[38] M. Thorwart, J. Eckel, E. R. Mucciolo, Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons, Phys. Rev. B, 2005, 72: 235320～235325.
[39] X. T. Liang, Non-Markovian dynamics and phonon decoherence of a double quantum dot charge qubit, Phys. Rev. B, 2005, 72: 245328～245332.
[40] U. Weiss, Quantum Dissipative Systems, 2nd ed., World Scientific, Singapore, 1999.
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