量子计算和量子关联在约瑟夫森结系统中的研究
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摘要
本论文分析讨论了在约瑟夫森系统中量子计算的实现和量子关联性质的研究。主要讨论集中在以下几方面的工作。
我们首先对量子计算领域做了一个简单的介绍。量子计算目前是一个非常庞大的学科,发展十分迅速。利用量子力学的基本原理,量子计算机的计算能力大大地超越了现有的经典计算机。利用量子计算的方式,我们可以解决类似大数因子化这样在经典计算框架中难以解决的任务。接着我们又介绍了约瑟夫森系统在量子计算中的应用与现状,包括两种最基本的约瑟夫森量子比特的实现。
我们详细描述了一个基于拓扑保护的约瑟夫森结阵列系统,在此系统之上建立整套量子计算处理的方案。用于量子计算的逻辑量子比特被编码在具有穿孔的阵列中。整个系统的量子比特的数量由孔洞的数量决定。通过调节沿着特定路径的磁通,系统的拓扑简并便可进行细微的改变。作为一套完整的量子计算的方案,我们展示了量子计算的基本元件—量子比特在该系统中的构成,以及最基本的单量子比特逻辑门和控制非量子逻辑门的实现。
我们研究了作为量子关联度量的一种方式—量子discord在带有DM相互作用参数的双量子比特海森堡XXZ模型中的性质。我们将该系统中的热量子discord与热纠缠做了比较。我们发现随着温度的增加,纠缠在临界温度时变为零值,而量子discord却渐进地逼近零值,但不会消失。与纠缠类似,作为一种可以利用的量子资源,量子discord在这个现象中体现出来的健壮性值得我进一步的利用。而对于DM参量,热量子discord约改变与热纠缠的改变趋势相反,这个特点为我们增强某系统的纠缠提供了一种可行的途径。另外,我们在研究中还发现,对于带有不同DM参数的该模型,带有Dx参量的情况比带有Dz参量的情况对控制量子discord更加有效。
最后,我们研究了具有以上特性的量子discord在一个真实约瑟夫森系统中的行为。我们发现,作为这样一个可在实验室中实现的系统,系统的量子discord和温度以及约瑟夫森耦合能EJ联系紧密。减小EJ或者降低温度,都可以增大系统的量子discord。并且,采用两个相同的约瑟夫森结来构建的系统和采用两个不同的约瑟夫森结来构建的系统,系统的量子discord在行为趋势上基本没有区别。为了调控系统的量子discord,我们发现,当温度较小,并且EJ也较小时,我们可以得到更高的量子discord,并且在这样的区域调控的作用也更加敏感。另外,相对于两个不同的约瑟夫森结情况,两个相同的约瑟夫森结情况在其它条件相同时,可以得到更高的系统量子discord,使这样一种量子资源能够更有机会得以利用。
Studies on the implementation of quantum computation and the properties of quan-tum correlation in Josephson junction systems are discussed in this dissertation. It mainly focuses on the following parts.
First, we give a brief introduction on quantum computation. Quantum computation is a wide field and develops rapidly. Take the advantage of principles of quantum mechanics, the computational power of quantum computers exceed classical computers largely. Based on quantum computation, lots of hard work in classical computation such as large num-ber factoring can be solved efficiently. Subsequently, we present the status of Josephson junction system and its applications in quantum computation, including two basic imple-mentations of quantum bit based on Josephson junction systems.
We describe a topological protected Josephson junction array system. And propose a complete quantum computation scheme on it. The logic qubit for quantum computation is encoded in a punctured array. The number of qubits depends on the number of holes in this system. The topological degeneracy is lightly shifted by tuning the flux along specific paths. As a complete quantum computation scheme, we show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.
We study the properties of quantum discord (QD) which is a kind of measurement of quantum correlation in a two-qubit Heisenberg XXZ system with DM interaction. We compare the thermal QD with thermal entanglement in this system and find that QD decrease asymptotically to zero with temperature while entanglement decreases to zero at the point of critical temperature. This phenomenon shows the robust of QD and that QD can be used as a resource. We find behaviors of QD vary opposite to entanglement with some DM parameters and this possibly offers a potential solution to enhance entanglement of certain systems. We also show that tunable parameter Dx is more efficient than parameter Dz in most regions for controlling the QD.
Finally, we investigate QD with exotic features discussed above in a two-qubit real Josephson-junction system. We find that QD of such a system in lab correlates closely with temperature and Josephson coupling energy EJ. QD can be enhanced while lowering Ej or temperature. The behavior trends of identical qubits system and distinct qubits system maintain the same. We can get a higher QD when making EJ and temperature smaller. Also we can take a good chance to use such quantum resource when two qubits are identical since in this case we can get more quantum discords.
我们首先对量子计算领域做了一个简单的介绍。量子计算目前是一个非常庞大的学科,发展十分迅速。利用量子力学的基本原理,量子计算机的计算能力大大地超越了现有的经典计算机。利用量子计算的方式,我们可以解决类似大数因子化这样在经典计算框架中难以解决的任务。接着我们又介绍了约瑟夫森系统在量子计算中的应用与现状,包括两种最基本的约瑟夫森量子比特的实现。
我们详细描述了一个基于拓扑保护的约瑟夫森结阵列系统,在此系统之上建立整套量子计算处理的方案。用于量子计算的逻辑量子比特被编码在具有穿孔的阵列中。整个系统的量子比特的数量由孔洞的数量决定。通过调节沿着特定路径的磁通,系统的拓扑简并便可进行细微的改变。作为一套完整的量子计算的方案,我们展示了量子计算的基本元件—量子比特在该系统中的构成,以及最基本的单量子比特逻辑门和控制非量子逻辑门的实现。
我们研究了作为量子关联度量的一种方式—量子discord在带有DM相互作用参数的双量子比特海森堡XXZ模型中的性质。我们将该系统中的热量子discord与热纠缠做了比较。我们发现随着温度的增加,纠缠在临界温度时变为零值,而量子discord却渐进地逼近零值,但不会消失。与纠缠类似,作为一种可以利用的量子资源,量子discord在这个现象中体现出来的健壮性值得我进一步的利用。而对于DM参量,热量子discord约改变与热纠缠的改变趋势相反,这个特点为我们增强某系统的纠缠提供了一种可行的途径。另外,我们在研究中还发现,对于带有不同DM参数的该模型,带有Dx参量的情况比带有Dz参量的情况对控制量子discord更加有效。
最后,我们研究了具有以上特性的量子discord在一个真实约瑟夫森系统中的行为。我们发现,作为这样一个可在实验室中实现的系统,系统的量子discord和温度以及约瑟夫森耦合能EJ联系紧密。减小EJ或者降低温度,都可以增大系统的量子discord。并且,采用两个相同的约瑟夫森结来构建的系统和采用两个不同的约瑟夫森结来构建的系统,系统的量子discord在行为趋势上基本没有区别。为了调控系统的量子discord,我们发现,当温度较小,并且EJ也较小时,我们可以得到更高的量子discord,并且在这样的区域调控的作用也更加敏感。另外,相对于两个不同的约瑟夫森结情况,两个相同的约瑟夫森结情况在其它条件相同时,可以得到更高的系统量子discord,使这样一种量子资源能够更有机会得以利用。
Studies on the implementation of quantum computation and the properties of quan-tum correlation in Josephson junction systems are discussed in this dissertation. It mainly focuses on the following parts.
First, we give a brief introduction on quantum computation. Quantum computation is a wide field and develops rapidly. Take the advantage of principles of quantum mechanics, the computational power of quantum computers exceed classical computers largely. Based on quantum computation, lots of hard work in classical computation such as large num-ber factoring can be solved efficiently. Subsequently, we present the status of Josephson junction system and its applications in quantum computation, including two basic imple-mentations of quantum bit based on Josephson junction systems.
We describe a topological protected Josephson junction array system. And propose a complete quantum computation scheme on it. The logic qubit for quantum computation is encoded in a punctured array. The number of qubits depends on the number of holes in this system. The topological degeneracy is lightly shifted by tuning the flux along specific paths. As a complete quantum computation scheme, we show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.
We study the properties of quantum discord (QD) which is a kind of measurement of quantum correlation in a two-qubit Heisenberg XXZ system with DM interaction. We compare the thermal QD with thermal entanglement in this system and find that QD decrease asymptotically to zero with temperature while entanglement decreases to zero at the point of critical temperature. This phenomenon shows the robust of QD and that QD can be used as a resource. We find behaviors of QD vary opposite to entanglement with some DM parameters and this possibly offers a potential solution to enhance entanglement of certain systems. We also show that tunable parameter Dx is more efficient than parameter Dz in most regions for controlling the QD.
Finally, we investigate QD with exotic features discussed above in a two-qubit real Josephson-junction system. We find that QD of such a system in lab correlates closely with temperature and Josephson coupling energy EJ. QD can be enhanced while lowering Ej or temperature. The behavior trends of identical qubits system and distinct qubits system maintain the same. We can get a higher QD when making EJ and temperature smaller. Also we can take a good chance to use such quantum resource when two qubits are identical since in this case we can get more quantum discords.
引文
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[3]DEUTSCH D. Quantum theory, the church-turing principle and the universal quan-tum computer.[J]. Proc. R. Soc. Lond. A,1985,400:97.
[4]SHOR P W. Algorithms for quantum computation:discrete logarithms and factor-ing. [J]. Annual Symposium on Foundations of Computer Science, IEEE Press, Los Alamitos, CA,1994.
[5]NIELSEN M A. Quantum information theory [J]. quant-ph/0011036,2000.
[6]EKERT A, JOZSA R. Quantum computation and shor's factoring algorithm[J]. Rev. Mod. Phys.,1996,68:733.
[7]KITAEV A Y. Fault-tolerant quantum computation by anyons[J]. arXiv e-print quant-ph/9707021,1997.
[8]RAUSSENDORF H J, R.& BRIEGEL. A one-way quantum computer.[J]. Physical Review Letters,2001,86:5188.
[9]GLADCHENKO S, OLAYA D, DUPONT-FERRIER E, et al. Superconducting nanocircuits for topologically protected qubits[J]. Nat Phys,2009,5(1):48-53.
[10]HANSON R, KOUWENHOVEN L P, PETTA J R, et al. Spins in few-electron quan-tum dots[J]. Reviews of Modern Physics,2007,79(4):1217.
[11]PORRAS D, CIRAC J I. Effective quantum spin systems with trapped ions[J]. Phys-ical Review Letters,2004,92(20):207901.
[12]TRAUZETTEL B, BULAEV D V, LOSS D, et al. Spin qubits in graphene quantum dots[J]. Nat Phys,2007,3(3):192-196.
[13]ZUREK W H. Decoherence, einselection, and the quantum origins of the classical[J]. Rev. Mod. Phys.,2003,75:715.
[14]YURIY MAKHLIN A S, GERD SCHON. Quantum-state engineering with josephson-junction devices[J]. REVIEWS OF MORDEN PHYSICS,2001,73:357.
[15]ARNESEN M C, BOSE S, VEDRAL V. Natural thermal and magnetic entanglement in the 1D heisenberg model[J]. Physical Review Letters,2001,87(1):017901.
[16]WANG X. Threshold temperature for pairwise and many-particle thermal entangle-ment in the isotropic heisenberg model[J]. Physical Review A,2002,66(4):044305.
[17]HORODECKI R, HORODECKI P, HORODECKI M, et al. Quantum entangle-ment[J]. Reviews of Modern Physics,2009,81(2):865.
[18]OLLIVIER H, ZUREK W H. Quantum discord:A measure of the quantumness of correlations[J]. Physical Review Letters,2001,88(1):017901.
[19]KNILL E, LAFLAMME R. Power of one bit of quantum information[J]. Physical Review Letters,1998,81(25):5672.
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