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量子纠错码[[7,1,4]]_p(p>3)存在性的图论构造方法 被引量：2

Existence of quantum codes [[7,1,4]] p(p > 3) via graphs
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摘要 利用由Schingemann和Werner两人提出的构造量子纠错码的图论方法,证明了量子纠错码[[7,1,4]]p(p>3)的存在性。 The existence of quantum stabilizer with parameters [[n, k, d]]p = [[7, 1,4]]p is showed for all primes （p 〉 3） by using graph machinery, given by Schingemann and Wemer, with a little number theory and combinatorics.
作者 程茜 于慧
机构地区 青海师范大学数学与信息科学系 大连交通大学数理系
出处 《计算机工程与应用》 CSCD 2012年第22期48-50,83,共4页 Computer Engineering and Applications
基金 青海省科技项目(No.2011-Z-734) 青海省自然科学基金资助项目(No.2011-Z-756) 青海师范大学青年创新基金项目(No.2012-4-13)
关键词 非二元量子码 量子稳定子码 对称矩阵 nonbinary quantum codes quantum stabilizer codes symmetric matrix
分类号 O151.24 [理学—基础数学] O413 [理学—理论物理]
  • 相关文献

参考文献11

  • 1Shor P W.Scheme for reducing decoherence in quan- tum memory[J].Phys Rev A, 1995,52.
  • 2Steane A M.Multiple particle interference and quantum error correction[C]//Proc Roy Soc London, 1996, 452: 2551-2557.
  • 3Calderbank A R, Rains E M, Shor P M, et al.Quantum error correction via codes over GF (4)[J].IEEE Trans on Inform Theory, 1998,44: 1369-1387.
  • 4Ashikhim A, Knill E.Non-binaryquantum stabilizer codes[J]. IEEE Trans on Inform Theory,2001,47 : 3065-3072.
  • 5Matsumoto R, Uyematsu T.Constructing quantum error- correcting codes for pm-state systems from classical error-correcting codes: 1999, quant-ph/9911011.
  • 6Rains E M.Nonbinary quantum codes[J].IEEE Trans on Inform Theory, 1999,45:1827-1832.
  • 7Schlingermann D, Werner R F.Quantum error-correctingcodes associated with graphs[J].Phys Rev A,2001,65.
  • 8Feng K Q.Quantum codes [[6,2,3]]p and [[7,3,3]]p (p≥3)exist[J].IEEE Trans on Inform Theory, 2002, 48: 2384-2391.
  • 9Grassl M, Klappenecker A, R0tteler M.Graph, quadratic forms, and quantum codes[C]//Proc IEEE Int Symp In- formation Theory,Lausanne,Swizerland,June/July 2002.
  • 10刘太琳,温巧燕,刘子辉.非二元量子循环码的一种图论方法构造[J].中国科学（E辑）,2005,35(6):588-596. 被引量：7

二级参考文献11

  • 1Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299:802～803.
  • 2Shor P W. Scheme for reducing decoherence in quantum memory. Phys Rev A, 1995, 52:2493.
  • 3Steane A M. Multiple particle interference and quantum error correction. Proc Roy Soc London A, 1996,452:2551～2557.
  • 4Calderbank A R, Rains E M, Shot P W, et al. Quantum error correction via codes over GF(4). IEEE Trans Inform Theory, 1998, 44(7): 1369～1387.
  • 5Ashikhim A, Knill E. Non-binary quantum stabilizer codes. IEEE Trans Inform Theory, 2001, 47(11):3065～3072.
  • 6Matsumoto R, Uyematsu T. Constructing quantum error-correcting codes for pm-state sysetems from classical error-correcting codes. 1999, quant-ph/9911011.
  • 7Rains E M. Nonbinary quantum codes. IEEE Trans Inform Theory, 1999, 45(9): 1827～1832.
  • 8Schlingemann D, Werner R F. Quantum error-correcting codes associated with graphs. Phys Rev A, 2001,65:no.012308.quant-ph/0012111.
  • 9Feng K Q, Quantum codes [[6, 2, 3]]p and [[7, 3, 3]]p(p ≥ 3) exist. IEEE Trans Inform Theory, 2002,48(8): 2384～2391.
  • 10Knill E, Laflamme R. A theory of quantum error-correcting codes. Phys Rev A, 1997, 55:900～911.

共引文献6

同被引文献14

  • 1刘太琳,温巧燕,刘子辉.非二元量子循环码的一种图论方法构造[J].中国科学（E辑）,2005,35(6):588-596. 被引量：7
  • 2Shor P W. Scheme for reducing decoherence in quantum memory [J]. Physical Review A, 1995, 52(4): 2493-2496.
  • 3Steane A M. Multiple particle interference and quantum error correction[J]. Proceedings of the Royal Society of London Series A, 1996, 452(1954): 2551-2557.
  • 4Calderbank A R, et al. Quantum error correction via codes over GF(4)[J], IEEE Transactions on Information Theory, 1998,44(4): 1369-1387.
  • 5Schlingermann D, Werner R F. Quantum error-correcting codes associated with graphs [J]. Physical Review A, 2002, 65(1): 012308- 012315.
  • 6Feng K Q. Quantum codes [[6, 2,3]]p and [[7,3,3]]p (p > 3) exist [J]. IEEE Transactions on Information Theory, 2002, 48(8): 2384- 2391.
  • 7P. W. Shor. Scheme for reducing decoherence in quantum memory[J]. Physical Review A, 1995, 52: 2493.
  • 8A. M. Steane. Multiple particle interference and quantum error correction[J]. Proceedings of The Royal Society of London Series A, 1996,452 .. 2551 -- 2557.
  • 9A. R. Calderbank et al. Quantum error correction via codes over GF(4)[J]. IEEE Transactions on Information Theory, 1998, 44(4) : 1369 --1387.
  • 10D. Schlingermann, R. F. Werner. Quantum error- correcting codes associated with graphs[J]. Physical Review A, 2002, 65 ( 1 ) : 012308.

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计算机工程与应用
2012年 第22期

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