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)

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.

Cite this article

TIAN Jia-xin1 , LIU Wen-qing1 , SONG Yan-hong1 , XUAN Ya-nan1 , LI Jun-fang2* , YAO Ye-feng1* , WEI Da-xiu1* . Implementation of Deutsch Algorithm Using Para-Hydrogen Induced Polarization
[J]. Chinese Journal of Magnetic Resonance, 2015
, 32(4) : 618 -627 . DOI: 10.11938/cjmr20150407

References

 


[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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