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Based on the quantum error-correction codes and concatenation, quantum logical gates can be implemented transversally, which is called the fault-tolerant quantum computation. Clifford gates can be directly and fault-tolerantly performed, but they cannot reach universal quantum computation. How to implement the non-Clifford gate fault-tolerantly is a vital technique in fault-tolerant universal quantum computation. Here the magic state is selected to help the implementing of the non-Clifford gate transversally. Based on the non-stabilizer state cos θi|0>+sinθi|1>, circuits which can execute 2θi rotation around X-axis and Z-axis fault-tolerantly are proposed. Then new non-stabilizer states in this form are developed and produced from the distilled magic state. By using these states, a number of non-Clifford gates can be performed transversally, which makes profound implication in fault-tolerant quantum computation. We calculate the number of the non-stabilizer states needed for simulating the desired rotation operations, which is less than that in previous protocols.
[1] Sun J, Lu S F, Liu F, Yang L P 2012 Chin. Phys. B 21 010306
[2] Chen W, Xue Z Y, Wang Z D, Shen R 2014 Chin. Phys. B 23 030309
[3] Li T, Bao W S, Lin W Q, Zhang H, Fu X Q 2014 Chin. Phys. Lett. 31 050301
[4] Li H Y, Wu C W, Chen Y B, Lin Y G, Chen P X, Li C Z 2013 Chin. Phys. B 22 110305
[5] Wang X X, Zhang J Q, Yu Y F, Zhang Z M 2011 Chin. Phys. B 20 110306
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[9] Gottesman D 1997 Ph. D. Dissertation (California: Caltech)
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[11] Xiao F Y, Chen H W 2010 Acta Phys. Sin. 60 080303 (in Chinese) [肖芳英, 陈汉武 2010 60 080303]
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[15] Jochym-O'connor T, Laflamme R 2014 Phys. Rev. Lett. 112 010505
[16] Paetznick A, Reichardt B W 2013 Phys. Rev. Lett. 111 090505
[17] Bravyi S, Kitaev A 2005 Phys. Rev. A 71 022316
[18] Duclos-Cianci G, Svore K M 2013 Phys. Rev. A 88 042325
[19] Howard M, Wallman J, Veitch V, Emerson J 2014 Nature 510 351
[20] Jochym-O'connor T, Yu Y, Helou B, Laflamme R 2013 Quantum Inf. Comput. 13 361
[21] Yu Y F, Zhang Z M 2013 Acta Sin. Quantum Opt. 19 330 (in Chinese) [於亚飞, 张智明 2013 量子光学学报 19 330]
[22] Reichardt B W 2005 Quantum Inf. Process 4 251
[23] Campbell E T, Anwar H, Browne D E 2012 Phys. Rev. X 2 041021
[24] Bravyi S, Haah J 2012 Phys. Rev. A 86 052329
[25] Anwar H, Campbell E T, Browne D E 2012 New J. Phys. 14 063006
[26] Meier A M, Eastin B, Knill E 2013 Quantum Inf. Comput. 13 195
[27] Reichardt B W 2009 Quantum Inf. Comput. 9 1030
[28] Jones C 2013 Phys. Rev. A 87 042305
[29] Campbell E T, Browne D E 2010 Phys. Rev. Lett. 104 030503
[30] Jones N C, Van M R, Fowler A G, McMahon P L, Kim J, Ladd T D, Yamamoto Y 2012 Phys. Rev. X 2 031007
[31] Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324
[32] Sun J G, He Y G 2003 J. Software 14 334 (in Chinese) [孙吉贵, 何雨果 2003 软件学报 14 334]
[33] Grover L K 1996 Proc. 28th ACM Symp. Theory of Comp. May 22-24, 1996, p212-219
[34] Bocharov A, Svore K M 2012 Phys. Rev. Lett. 109 190501
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[1] Sun J, Lu S F, Liu F, Yang L P 2012 Chin. Phys. B 21 010306
[2] Chen W, Xue Z Y, Wang Z D, Shen R 2014 Chin. Phys. B 23 030309
[3] Li T, Bao W S, Lin W Q, Zhang H, Fu X Q 2014 Chin. Phys. Lett. 31 050301
[4] Li H Y, Wu C W, Chen Y B, Lin Y G, Chen P X, Li C Z 2013 Chin. Phys. B 22 110305
[5] Wang X X, Zhang J Q, Yu Y F, Zhang Z M 2011 Chin. Phys. B 20 110306
[6] Bacon D, Kempe J, Lidar D A, Whaley K B 2000 Phys. Rev. Lett. 85 1758
[7] Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1675 (in Chinese) [张权, 张尔扬, 唐朝京 2002 51 1675]
[8] Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199
[9] Gottesman D 1997 Ph. D. Dissertation (California: Caltech)
[10] Li Z, Xing L J 2013 Acta Phys. Sin. 62 130306 (in Chinese) [李卓, 刑莉娟 2013 62 130306]
[11] Xiao F Y, Chen H W 2010 Acta Phys. Sin. 60 080303 (in Chinese) [肖芳英, 陈汉武 2010 60 080303]
[12] Nielsen M A , Chuang I L 2000 Quantum Computation and Quantum Information (Vol.1) (Cambridge, England: Cambridge University Press) p179
[13] Eastin B 2013 Phys. Rev. A 87 032321
[14] Landahl A J, Cesare C 2013 Preprint arXiv: 1302.3240
[15] Jochym-O'connor T, Laflamme R 2014 Phys. Rev. Lett. 112 010505
[16] Paetznick A, Reichardt B W 2013 Phys. Rev. Lett. 111 090505
[17] Bravyi S, Kitaev A 2005 Phys. Rev. A 71 022316
[18] Duclos-Cianci G, Svore K M 2013 Phys. Rev. A 88 042325
[19] Howard M, Wallman J, Veitch V, Emerson J 2014 Nature 510 351
[20] Jochym-O'connor T, Yu Y, Helou B, Laflamme R 2013 Quantum Inf. Comput. 13 361
[21] Yu Y F, Zhang Z M 2013 Acta Sin. Quantum Opt. 19 330 (in Chinese) [於亚飞, 张智明 2013 量子光学学报 19 330]
[22] Reichardt B W 2005 Quantum Inf. Process 4 251
[23] Campbell E T, Anwar H, Browne D E 2012 Phys. Rev. X 2 041021
[24] Bravyi S, Haah J 2012 Phys. Rev. A 86 052329
[25] Anwar H, Campbell E T, Browne D E 2012 New J. Phys. 14 063006
[26] Meier A M, Eastin B, Knill E 2013 Quantum Inf. Comput. 13 195
[27] Reichardt B W 2009 Quantum Inf. Comput. 9 1030
[28] Jones C 2013 Phys. Rev. A 87 042305
[29] Campbell E T, Browne D E 2010 Phys. Rev. Lett. 104 030503
[30] Jones N C, Van M R, Fowler A G, McMahon P L, Kim J, Ladd T D, Yamamoto Y 2012 Phys. Rev. X 2 031007
[31] Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324
[32] Sun J G, He Y G 2003 J. Software 14 334 (in Chinese) [孙吉贵, 何雨果 2003 软件学报 14 334]
[33] Grover L K 1996 Proc. 28th ACM Symp. Theory of Comp. May 22-24, 1996, p212-219
[34] Bocharov A, Svore K M 2012 Phys. Rev. Lett. 109 190501
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