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Quantum walk is a typical quantum computing model which is receiving significant attention in recent years from theory researchers. In this paper, we prove that the two major formulations for discrete quantum walks, coined and scattering, are unitarily equivalent on star graph. We then propose a new quantum search algorithm on star graph based on the scattering quantum walk. It is shown that the temporal complexity of the algorithm is the same as that in Grover algorithm, but success probability is greater than that in Grover algorithm when the objects are more than one third of total items.
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Keywords:
- coined quantum walk /
- scattering quantum walk /
- grover algorithm
[1] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687
[2] Hillery M, Bergou J, Feldman E 2003 Phys. Rev. A 68 032314
[3] Feldman E, Hillery M 2004 Physics Letters A 324 277
[4] Feldman E, Hillery M 2007 Physics A: Mathematical and Theoretical 40 11343
[5] Feldman E, Hillery M, H W Lee 2010 Phys. Rev. A 82 040301
[6] Feldman E, Hillery M 2005 Contemporary Mathematics 381 71
[7] Reitzner D, Hillery M, Feldman E 2009 Phys. Rev. A 79 012323
[8] Li P C, Li S Y 2007 CAAL Transactions on Intelligent Systems 1 35 (in Chinese) [李盼池, 李士勇 2007 智能系统学报 1 35]
[9] Krovi H, Brun T A 2007 Phys. Rev. A 75 062332
[10] Jian R Y, An H. B 2007 Operator Theory Guide of analytic function space (First Edition) (Beijing: Science Press) p7 (in chinese) [蹇人宜, 安恒斌著2007解析函数空间上的算子理论导引(第一版) (北京: 科学出版社)第7页]
[11] Daniel Reitzner, Daniel Nagaj, Vladimir Buzek 2011 Acta Physica Slovaca 61 603
[12] Ambainis A 2004 SIAM Journal on Computing 37 210
[13] Childs A M, Eisenberg J M 2003 arXiv:0311038[quant-ph]
[14] Shenvi N, Kempe J, Whaley K B 2003 Phys. Rev. A 67 052307
[15] Chen Y P, Zhang K Y, Xu Z 2006 Matrix Theory (Third edition) (Xi'an: Northwestern University Press) p60 (in chinese) [陈云鹏, 张凯院, 徐仲 2006 矩阵论(第三版) (西安: 西北工业大学出版社) 第60 页]
[16] Grover L K 1997 Physical Review Letters 79 325
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[1] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687
[2] Hillery M, Bergou J, Feldman E 2003 Phys. Rev. A 68 032314
[3] Feldman E, Hillery M 2004 Physics Letters A 324 277
[4] Feldman E, Hillery M 2007 Physics A: Mathematical and Theoretical 40 11343
[5] Feldman E, Hillery M, H W Lee 2010 Phys. Rev. A 82 040301
[6] Feldman E, Hillery M 2005 Contemporary Mathematics 381 71
[7] Reitzner D, Hillery M, Feldman E 2009 Phys. Rev. A 79 012323
[8] Li P C, Li S Y 2007 CAAL Transactions on Intelligent Systems 1 35 (in Chinese) [李盼池, 李士勇 2007 智能系统学报 1 35]
[9] Krovi H, Brun T A 2007 Phys. Rev. A 75 062332
[10] Jian R Y, An H. B 2007 Operator Theory Guide of analytic function space (First Edition) (Beijing: Science Press) p7 (in chinese) [蹇人宜, 安恒斌著2007解析函数空间上的算子理论导引(第一版) (北京: 科学出版社)第7页]
[11] Daniel Reitzner, Daniel Nagaj, Vladimir Buzek 2011 Acta Physica Slovaca 61 603
[12] Ambainis A 2004 SIAM Journal on Computing 37 210
[13] Childs A M, Eisenberg J M 2003 arXiv:0311038[quant-ph]
[14] Shenvi N, Kempe J, Whaley K B 2003 Phys. Rev. A 67 052307
[15] Chen Y P, Zhang K Y, Xu Z 2006 Matrix Theory (Third edition) (Xi'an: Northwestern University Press) p60 (in chinese) [陈云鹏, 张凯院, 徐仲 2006 矩阵论(第三版) (西安: 西北工业大学出版社) 第60 页]
[16] Grover L K 1997 Physical Review Letters 79 325
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