利用仲氢诱导极化技术实现 Deutsch算法

田佳欣1; 刘文卿1; 宋艳红1; 轩亚楠1; 李军方2*; 姚叶锋1*; 魏达秀1*

doi:10.11938/cjmr20150407

波谱学杂志 >

2015 , Vol. 32 >Issue 4: 618 - 627

DOI: https://doi.org/10.11938/cjmr20150407

研究论文

利用仲氢诱导极化技术实现 Deutsch算法

田佳欣1 ,
刘文卿1 ,
宋艳红1 ,
轩亚楠1 ,
李军方2* ,
姚叶锋1* ,
魏达秀1*

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1. 华东师范大学物理系，上海市磁共振重点实验室，上海 200062；
2. 中国科学院上海有机化学研究所，上海 200032

田佳欣(1988-)，女，山西太原人，硕士研究生，无线电物理专业． *通讯联系人：李军方，电话： 021-54925475， E-mail: junfangli@sioc.ac.cn；姚叶锋，电话： 021-62234328， E-mail: yfyao@phy.ecnu.edu.cn；魏达秀，电话： 021-62233281， E-mail: dxwei@phy.ecnu.edu.cn.

收稿日期: 2015-03-02

修回日期: 2015-11-03

网络出版日期: 2015-12-05

基金资助

国家自然科学基金资助项目(11005039)

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Implementation of Deutsch Algorithm Using Para-Hydrogen Induced Polarization

TIAN Jia-xin1 ,
LIU Wen-qing1 ,
SONG Yan-hong1 ,
XUAN Ya-nan1 ,
LI Jun-fang2* ,
YAO Ye-feng1* ,
WEI Da-xiu1*

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1. Shanghai Key Laboratory of Magnetic Resonance, Department of Physics, East China Normal University, Shanghai 200062, China;
2. Shanghai Institute of Organic Chemistry, Shanghai 200032, China

*Corresponding author： LI Jun-fang, Tel: +86-21-54925475, E-mail: junfangli@sioc.ac.cn; YAO Ye-feng, Tel: +86-21-62234328, E-mail: yfyao@phy.ecnu.edu.cn; WEI Da-xiu, Tel: +86-21-62233281, E-mail: dxwei@phy.ecnu.edu.cn.

Received date: 2015-03-02

Revised date: 2015-11-03

Online published: 2015-12-05

Supported by

国家自然科学基金资助项目(11005039)

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摘要

核磁共振系统是实现量子计算的有效物理体系之一．但是随着量子位数的不断增加，运用核磁共振技术实现计算任务存在明显的局限性，原因之一是量子计算的初始态—赝纯态，随着量子位数的增加，信号指数性的衰减，量子位数越多制备赝纯态所需的脉冲序列越复杂，越不容易实现，不利于量子位数的扩展；另外，由于核磁共振中制备的赝纯态实际上也是一种混合态，用于实现量子信息任务时存在一定的争议．该文介绍的利用仲氢诱导极化技术(PHIP)制备出的实验初态，能够解决初态处于混合态的问题，并且信号强度显著增强，作者利用此态实现了 ALTADENA 条件下的两量子位的 Deutsch-Jozsa 量子算法和 PASADENA 条件下的三量子位的 Deutsch-Like 量子算法．

关键词： 核磁共振(NMR); 仲氢诱导极化技术(PHIP); ALTADENA; PASADENA; Deutsch算法

本文引用格式

田佳欣1 , 刘文卿1 , 宋艳红1 , 轩亚楠1 , 李军方2* , 姚叶锋1* , 魏达秀1* . 利用仲氢诱导极化技术实现 Deutsch算法
[J]. 波谱学杂志, 2015 , 32(4) : 618 -627 . DOI: 10.11938/cjmr20150407

Abstract

The NMR system is one of the physical systems that can be used to realize quantum computation. However, NMR-based quantum computing could have many drawbacks with increasing qubit number. One of the underlying reasons is that the signal of pseudo-pure state decreases exponentially with increasing qubit number. Besides, the process required to prepare a pseudo-pure state becomes more complicated as the spin system gets larger. Furthermore, the pseudo-pure state in NMR system is in fact a mixed state, making it difficult to realize quantum entanglement. In this paper, we used parahydrogen induced polarization (PHIP) technique to prepare a genuine pure state for NMR quantum computation with significantly enhanced signal intensity. The initial state was applied to implement a two-qubit Deutsch-Jozsa algorithm and a three-qubit Deutsch-like algorithm.

Key words： nuclear magnetic resonance (NMR); parahydrogen induced polarization (PHIP); ALTADENA; PASADENA; Deutsch algorithm

参考文献

[1] Bowers C R, Weitekamp D P. Transformation of symmetrization order to nuclear-spin magnetization by chemical reaction and nuclear magnetic resonance[J]. Phys Rev Lett, 1986, 57(21): 2 645－2 648

[2] Natterer J, Bargon J. Parahydrogen induced polarization[J]. Prog Nucl Magn Reson Spectrosc, 1997, 31(4): 293－315.

[3] Duckett S B, Sleigh C J. Applications of the parahydrogen phenomenon: A chemical perspective[J]. Prog Nucl Magn Reson Spectrosc, 1999, 34 (1): 71－92.

[4] Duckett S B, Blazina D. The study of inorganic systems by NMR spectroscopy in conjunction with parahydrogen induced polarisation[J]. Eur J Inorg Chem, 2003, 2 003(16): 2 901－2 912.

[5] Jones J A. NMR quantum computation[J]. Prog NMR Spectrosc, 2001, 32(29): 325－360.

[6] Ernst R R, Bodenhausen G, Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions[M]. Oxford: Oxford Univ Press, 1988.

[7] Levitt M H. Spin Dynamics: Basics of Nuclear Magnetic Resonance (2nd ed) [M]. USA: Wiley, 2008.

[8] Chen H W, Lu D W, Chong B, et al. NMR experimental demonstration of probabilistic quantum cloning[J]. Phys Rev Lett, 2011, 106(18): 180404.

[9] Chuang I L, Gershenfeld N, Kubinec M. Experimental implementation of fast quantum searching[J]. Phys Rev Lett, 1998, 80(215): 3 408－3 411.

[10] Feng G R, Xu G F, Long G L. Experimental realization of nonadiabatic holonomic quantum computation[J]. Phys Rev Lett, 2013, 110(19): 190501.

[11] Unruh W G. Maintaining coherence in quantum computers[J]. Phys Rev, 1995, 51(2): 992－997.

[12] Chuang I L, Laflamme R, Shor P, et al. Quantum computers, factoring and decoherence[J]. Science, 1995, 273(5 242): 1 633－1 635.

[13] Landauer R. Dissipation and noise immunity in computation and communication[J]. Nature, 1988, 335(6 193): 779－784.

[14] Landauer R. Is quantum mechanics useful[J]. Phil Trans R Soc Lond A, 1995, 353(1 703): 367－376.

[15] Palma G M, Suominen, K A, Ekert A K. Quantum computers and dissipation[J]. Proc R Soc Lond A, 1996, 452(1 946): 567－584.

[16] DiVincenzo D P. The physical implementation of quantum computation[J]. Fort der Physik, 2000, 48(9－11): 771－783.

[17] Feynman R. Simulating physics with computers[J]. Int J Theor Phys, 1982, 21(6－7): 467－488.

[18] Jones J A. NMR quantum computation: A critical evaluation[J]. Fort der Physik, 2000, 48(9－11): 909－924.

[19] Lu Y, Feng G R, Li Y S, et al. Experimental digital quantum simulation of temporal-spatial dynamics of interacting fermion system[J]. Science Bulletin, 2015, 60(2): 241－248.

[20] Gershenfeld N A, Chuang I L. Bulk spin-resonance quantum computation[J]. Science, 1997, 275 (5 298): 350－356.

[21] Knill E, Chuang I, Laflamme R. Effective pure states for computation[J]. Phys Rev A, 1997, 57(5): 3 348－3 363.

[22] Knill E, Laflamme R, Martinez R, et al. An algorithmic benchmark for quantum information processing[J]. Nature, 2000, 404(6 776): 368－370.

[23] Gui L L, Zhou Y F, Jin J Q, et al. Density matrix in quantum mechanics and distinctness of ensembles having the same compressed density matrix[J]. Found Phys, 2006, 36(4): 1 217－1 243.

[24] Anwar M S, Blazina D, Carteret H A, et al. Implementing Grover’s quantum search on a para-hydrogen based pure state NMR quantum computer[J]. Chem Phys Lett, 2004, 400(1－3): 94－97.

[25] Deutsch D, Jozsa R. Rapid solution of problems by quantum computation[J]. Proc R Soc Lond A, 1992, 439(1 907): 553－558.

[26] Dorai K, Arvind, Kumar A. Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level on an NMR quantum-information processor[J]. Phys Rev A, 2002, 63(3): 034101.

[27] Wei D, Luo J, Sun X, et al. Realization of Deutsch-like algorithm using ensemble computing[J]. Phys Lett A, 2003, 319(3－4): 267－272.

[28] Bowers C R, Weitekamp D P. Transformation of symmetrization order to nuclear-spin magnetization by chemical reaction and nuclear magnetic resonance[J]. Phys Rev Lett, 1986, 57(21): 2 645－2 648.

[29] Koch A, Ulrich C, Bargon J. In situ NMR observation of tin trichloride-activated rhodium dihydride complexes using parahydrogen induced polarization[J]. Tetrahedron, 2000, 56(20): 3 177－3 179.

[30] Deutsch D, Jozsa R. Rapid solution of problems by quantum computation[J]. Proc R Soc Lond A, 1992, 439(1 907): 553－558.

[31] Cleve R, Ekert A, Macchiavello C, et al. Quantum algorithm revisited[J]. Proc R Soc Lon A, 1998, 454(1 960): 339－354.

[32] Wei D X, Yang X D, Luo J, et al. NMR experimental implementation of three-parties quantum superdense coding[J]. Chinese Sci Bull, 2004, 49(5): 423－426.

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