两类阿贝尔Cayley图上的完全状态转移
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摘要
完全状态转移在量子信息传输以及量子计算中有重要的应用,本文利用有限阶阿贝尔群上的特征、等价类,有理数域上的p-adic赋值等理论,通过计算得出两类有限阶阿贝尔群G=Z_4?Z_8,G=Z_8?Z_8上的Cayley图有完全状态转移。
The perfect state transfer(PST) is of great significance for its applications in quantum information transmission and quantum computation. In this paper,based on the theory of character and equivalent classes of the finite abelian group and that of the p-adic valuation on rational number filed, we obtain the fact that two classes of finite abelian groups G=Z_4?Z_8 and G=Z_8?Z_8 have the PST of Cayley graphs.
The perfect state transfer(PST) is of great significance for its applications in quantum information transmission and quantum computation. In this paper,based on the theory of character and equivalent classes of the finite abelian group and that of the p-adic valuation on rational number filed, we obtain the fact that two classes of finite abelian groups G=Z_4?Z_8 and G=Z_8?Z_8 have the PST of Cayley graphs.
引文
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[11] TAN Yingying,FENG Keqin,CAO Xiwang.Perfect state transfer on abelian Cayley graphs[J/OL].arXiv:1712.09260vl.
[12] 张爱仙,李江华,孙晓青.计算一类循环码的重要分布[J].西安理工大学学报,2015,31(2):180-182.ZHANG Aixian,LI Jianghua,SUN Xiaoqing.The weight distribution of a class of cyclic codes[J].Journal of Xi'an University of Technology,2015,31(2):180-182.
[2] CHRISTANDL M,DATTA N,DORLAS T,et al.Perfect state transfer of arbitrary state in quantum spin networks[J].Physical Review A,2005,71(3):032312.
[3] BERNASCONI A,GODSIL C,SEVERINI S.Quantum networks on cubelike graphs[J].Physical Review A,2008,78(5):052320.
[4] GODSIL C.Periodic graphs[J].The Electronic Journal of Combinatorics,2011,18(1):23.
[5] GODSIL C.State transfer on graphs[J].Discrete Mathematics,2012,312(1):129-147.
[6] GODSIL C.When can perfect state transfer occur?[J].Electronic Journal of Linear Algebra,2012,23:877-890.
[7] COUTINHO G,GODSIL C,GUO K,et al.Perfect state transfer on distance-regular graphs and association schemes[J].Linear Algebra and its Applications,2015,478:108-130.
[8] JOHNSTON N,KIRKLAND S,PLOSKER S,et al.Perfect state transfer using Hadamard diagonalizable graphs[J].Linear Algebra and its Applications,2017,531:373-398.
[9] BASIC M.Characterization of quantum circulant networks having perfect state transfer[J].Quantum Information Process,2013,12(1):345-364.
[10] CHEUNG W,GODSIL C.Perfect state transfer in cubelike graphs[J].Linear Algebra and its Applications,2011,435(10):2468-2474.
[11] TAN Yingying,FENG Keqin,CAO Xiwang.Perfect state transfer on abelian Cayley graphs[J/OL].arXiv:1712.09260vl.
[12] 张爱仙,李江华,孙晓青.计算一类循环码的重要分布[J].西安理工大学学报,2015,31(2):180-182.ZHANG Aixian,LI Jianghua,SUN Xiaoqing.The weight distribution of a class of cyclic codes[J].Journal of Xi'an University of Technology,2015,31(2):180-182.