核磁共振中的量子控制

李俊; 崔江煜; 杨晓东; 罗智煌; 潘健; 余琦; 李兆凯; 彭新华; 杜江峰

doi:10.7498/aps.64.167601

摘要

近年来, 随着量子信息科学的发展, 对由量子力学原理描述的微观世界的主动调控已成为重要的前沿研究领域. 为构造实际的量子信息处理器, 一个关键的挑战是: 如何对处于噪声环境下的量子体系实现一系列高精度的任意操作, 以完成目标量子信息处理任务. 为此, 人们将经典系统控制论的思想方法延伸到量子体系的领域, 提出了大量的量子控制方法以及相关的数值技术(如量子优化控制、量子反馈控制等), 并取得了丰富的研究成果. 核磁共振自旋体系具备成熟的系统理论和操控技术, 为量子控制方法的实用性研究提供了优秀的实验测试平台. 因此, 基于核磁共振的量子控制成为量子控制领域的重要方向. 本文简要介绍了量子控制的基本概念和方法; 从系统控制论的角度对核磁共振自旋体系的基本原理和重要控制任务做了阐述; 介绍了近些年来在该领域发展的相关控制方法及其应用; 对基于核磁共振体系的量子控制的进一步的研究做了几点展望.

关键词:

Abstract

With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.

Keywords:

作者及机构信息

1.
中国科学技术大学近代物理系, 合肥微尺度物质科学国家实验室, 合肥 230026;

2.
中国科学技术大学, 量子信息与量子科技前沿协同创新中心, 合肥 230026

基金项目: 国家重点基础研究发展规划(批准号: 2013CB921800, 2014CB848700)、国家杰出青年科学基金(批准号: 11425523)、国家自然科学基金 (批准号: 11375167, 11227901, 91021005)、中国科学院战略性先导科技专项(B)(批准号: XDB01030400)和高等学校博士学科点专项科研基金 (批准号: 20113402110044)资助的课题.

Authors and contacts

1.
Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;

2.
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2013CB921800, 2014CB848700), the National Natural Science Fund for Distinguished Young Scholars of China (Grant No. 11425523), the National Natural Science Foundation of China (Grant Nos. 11375167, 11227901, 91021005), the Strategic Priority Research Program (B) of Chinese Academy of Sciences (Grant No. XDB01030400), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113402110044).

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施引文献

[1]	Wiseman H M, Milburn G J 2010 Quantum Measurement and Control (Cambridge: Cambridge University Press)
[2]	Dong D, Petersen I R 2010 IET Control Theory Appl. 4 2651
[3]	Alessandro D D 2007 Introduction to Quantum Control and Dynamics (London: Chapman & Hall)
[4]	Brif C, Chakrabarti R, Rabitz H 2010 New J. Phys. 12 075008
[5]	Feynman R P 1982 Int. J. Theor. Phys. 21 467
[6]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[7]	Vandersypen L M K 2001 Ph. D. Dissertation (Stanford: Stanford University)
[8]	Vandersypen L M K, Chuang I L
[9]	Ryan C A, Negrevergne C, Laforest M, Knill E, Laflamme R 2008 Phys. Rev. A 78 012328
[10]	Chuang I, Vandersypen L, Zhou X, Leung D, Lloyd S 1998 Nature 393 143
[11]	Wu Z, Li J, Zheng W Q, Luo J, Feng M, Peng X H 2011 Phys. Rev. A 84 042312
[12]	Jones J, Mosca M, Hansen R 1998 Nature 393 344
[13]	Vandersypen L M K, Steffen M, Breyta G, Yannoni C S, Sherwood M H, Chuang I L 2001 Nature 414 883
[14]	Lu D W, Zhu J, Zou P, Peng X H, Yu Y H, Zhang S M, Chen Q, Du J F 2010 Phys. Rev. A 81 022308
[15]	Du J F, Xu N Y, Peng X H, Wang P F, Wu S F, Lu D W 2010 Phys. Rev. Lett. 104 030502
[16]	Peng X H, Wu S F, Li J, Suter D, Du J F 2010 Phys. Rev. Lett. 105 240405
[17]	Feng G R, Long G L, Laflamme R 2013 Phys. Rev. A 88 022305
[18]	Laflamme R, Knill E, Zurek W, Catasti P, Mariappan S 1998 Philos. Trans. R. Soc. London Ser. A 356 1941
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[20]	Negrevergne C, Mahesh T S, Ryan C A, Ditty M, Cyr-Racine F, Power W, Boulant N, Havel T, Cory D G, Laflamme R 2006 Phys. Rev. Lett. 96 170501
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[75]	Peng X H, Du J F, Dieter S 2005 Phys. Rev. A 71 012307
[76]	Li Z K, Zhou H, Ju C Y, Chen H W, Zheng W Q, Lu D W, Rong X, Duan C K, Peng X H, Du J F 2014 Phys. Rev. Lett. 112 220501
[77]	Peng X H, Luo Z H, Zheng W Q, Kou S P, Suter D, Du J F 2014 Phys. Rev. Lett. 113 080404
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[79]	Knill E, Chuang I, Laflamme R 1998 Phys. Rev. A 57 3348
[80]	Cory D G, Price M D, Havel T F 1998 Physica D 120 82
[81]	Schulman L J, Mor T, Weinstein Y 2005 Phys. Rev. Lett. 94 120501
[82]	Ryan C A, Moussa O, Baugh J, Laflamme R 2008 Phys. Rev. Lett. 100 140501
[83]	Fortunato E M, Pravia M A, Boulant N, Teklemariam G, Havel T F, Cory D G 2002 J. Chem. Phys. 116 7599
[84]	Jeffries C D 1963 Dynamic Nuclear Orientation (New York: Wiley)
[85]	Muus L T, Atkins P W, McLauchlan K A, Pedersen J B 1977 Chemically Induced Magnetic Polarization (Dordrecht: D. Reidel)
[86]	Li J, Lu D W, Luo Z H, Laflamme R, Peng X H, Du J F 2014 arXiv:1412.4146v1
[87]	Ernst R R, Bodenhausen G, Wokaun A 1987 Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford: Oxford University Press)
[88]	Sorensen O W 1989 Progress in NMR Spectroscopy 21 503
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[91]	Horn R A, Johnson C R 2013 Matrix Analysis (Cambridge: Cambridge University Press)
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