. ρ out. ε ρ in ρ out. . Shor 11 Grover 12. = Σ V μ ρ in. ε ρ in. ε. Liouville QED. A m ρ in. A n. 3 m n 22. = Σ. χ mn. = Σ χ mn. = Σ λ jk ρ k.

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Download ". ρ out. ε ρ in ρ out. . Shor 11 Grover 12. = Σ V μ ρ in. ε ρ in. ε. Liouville QED. A m ρ in. A n. 3 m n 22. = Σ. χ mn. = Σ χ mn. = Σ λ jk ρ k."

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1 /2010 /59 10 / ACTA PHYSICA SINICA Vol 59 No 10 October Chin Phys Soc * J PACC ε ρ in 1 3 ρ out ε ρ in ρ out Deutsch 10 ε Shor 11 Grover ρ out ρ out = ε ρ in = Σ V ρ in V 2 V Σ V V = 1 V ε Liouville QED A 2 ε ρ in = Σ χ mn A m ρ in 3 22 Hermit χ = χ mn ε ρ j ρ j ε ε ρ j = Σ λ j ρ 4 λ j 3 ε ρ j = Σ χ mn A m ρ j 5 * 2008J0219 yau@ xmu edu cn

2 A m ρ j = Σ β mn j ρ 6 ε CNOT CNOT 6 54 ε CNOT23 ρ 1 ρ 23 = I ε CNOT ρ 1 ρ 23 Σ β mn j χ mn = λ j 7 = ρ 1 ε CNOT ρ λ j χ mn ρ eq χ ε π /2 12 x -J 12 π /4 - π /2 x π /2 - π /2 3 x 12 π / x -J A n B 12 π /4 - π /2 x π /2 - π /2 3 y m m n ε s π /2 A AB y π / ε s I σ A σ B = ε s σ A σ B 8 12 I B ρ eq = I 1 z + I 2 z + B A x - I 1 y - + A ε s J 12 π /4 - I 2 y / 槡槡 2I 1 x I 2 z ε s I ( Σ σ A σ B ) = Σ ε s σ A σ B 9 m n - 槡 2I 1 y / 槡 2 = σ n - m n J 23 π /2 2 2n - I 2 z / 槡 2 + 2I 2 z + 2 槡 2I 1 x - 2 槡 2I 1 y / 槡 2 = σ 3 ε A 33 B A ε 34 2 π /2 3 σ 3 y - I 2 z / 槡 2-2I 2 z + 槡 3 1 /2 Hamilton H = Σ 3 i = 1 ω i I i z + Σ 3 i < j J ij I i z I j z 10 ω i i J ij i j 13 C CH 3 CH NH 2 COOH α 3 13 C J π / I 1 y / 槡 2 + 槡 2I 1 z = σ 1 π /2 x - I 2 z / 槡槡 2I 1 x π /2 3 x - I 2 z / 槡 2-2I 2 z - 2 槡 2I 1 x + 2 槡 2I 1 y / 槡 2 = σ I 1 x J 12 = 34 9 Hz J 23 = 54 0 Hz J 13 = 1 E 1 E Hz CNOT 槡 2 I2 y + I 3 z ( ) σ 1 1 E 1-2 槡 2I 1 y / 槡 2 = σ ρ eq = I 1 z + I 2 z + π /2 y I 1 x + + = σ 6 J 23 π /2 I 1 x I 2 z = σ 7 17 σ 1 σ σ 1

10 6839 2 3 2 3 2 3 Liouville 1 σ 1 σ 7 1 2 3 σ 1 σ 2 σ 3 σ 4 σ 5 σ 6 σ 7 E 1 I3 z I 2 z I3 y I 2 z I2 z I3 x I 2 z I2 z I3 x I 2 z I2 z I3 z I3 x I3 z I2 z I3 y I 1 x I 2 z I3 z I3 y I3 x E 23 E 23

3 Liouville 1 σ 1 σ σ 1 σ 2 σ 3 σ 4 σ 5 σ 6 σ 7 E 1 I3 z I 2 z I3 y I 2 z I2 z I3 x I 2 z I2 z I3 x I 2 z I2 z I3 z I3 x I3 z I2 z I3 y I 1 x I 2 z I3 z I3 y I3 x E 23 E 23 I 1 y E 23 I3 z I3 y I3 x I 1 z E 23 E 23 E 23 E 23 1 π /2 π x a σ 1 σ 4 π /2 x π /2 y σ 5 c 2 3 CNOT b σ 6 σ 7 1 a b σ 1 σ 7 1 c 2 3 CNOT s t = ms τ = ms CNOT χ CNOT 2 a CNOT χ Th 2 b F = 0 84 CNOT II XI YI ZI IX IY IZ XX YX ZX XY YY ZY XZ YZ ZZ 16 I X Y Z I Pauli 4 II = I I 2 CNOT χ Z a χ CNOT b χ Th 3 CNOT

4 J 2 J J 13 J 1 Plenio M BKnight P L 1996 Phys Rev A Yuan Z SChen Y AZhao BSchmiedmayer JPan J W 2008 Nature Kim M SCho J 2009 Science Du J FRong XZhao NWang YYang J HLiu R B 2009 Nature Yu TEberly J H 2009 Science Guo G CHan Z FHong P LWen H 2009 Chin Phys B Chen KPan J WPeng C ZRen J GYang BYi Z HZhou F 2009 Chin Phys B Cai X DPeng C ZRen J GYin JZhang HZhou F 2009 Acta Phys Sin in Chinese Lu H X 2007 Chin Phys Deutsch DJozsa R 1992 Proc Roy Soc Lond A Shor P W 1994 Proceedings of the 35th Annual Symposium on the Foundations of Computer ScienceUSANovember Santa Fep124 12Grover L K 1997 Phys Rev Lett Cory D GFahmy A FHavel T F 1997 Proc Natl Acad Sci U S A Barenco ABrun T ASchac RSpiller T P 1997 Phys Rev A Chuang I LVandersypen L M KZhou XLeung D WLloyd S 1998 Nature Fang X MFeng MGao K LShi LZhu X W 1999 Acta Phys Sin in Chinese Xue FDu J FFan Y MShi M JZhou X YHan R DWu J H 2002 Acta Phys Sin in Chinese Gershenfeld N AChuang I L 1997 Science Zhao BChen Y ABao X HStrassel TChuu C SJin X M Schmiedmayer JYuan Z SChen SPan J W 2009 Nat Phys Ai L YYang JZhang Z M 2008 Acta Phys Sin in Chinese Wang JYe LYu L B 2007 Chin Phys Negrevergne CMahesh T SRyan C ADitty MCyr-Racine FPower WBoulant NHavel TCory D GLaflamme R 2006 Phys Rev Lett Chuang I LNielsen M A 1997 J Mod Opt Poyatos J FCirac J IZoller P 1997 Phys Rev Lett Aguado MBrennen G KVerstraete FCirac J I 2008 Phys Rev Lett Childs A MChuang I LLeung D W 1998 Phys Rev A D Ariano G MPresti P L 2001 Phys Rev Lett O Brien J LPryde G JGilchrist AJameset D F VLangford N KRalph T CWhite A G 2004 Phys Rev Lett Riebe MKim KSchindler PMonz TSchmidt P OK rber T KH nsel WH ffner HRoos C FBlatt R 2006 Phys Rev Lett Ziman M 2008 Phys Rev A Schumacher B 1996 Phys Rev A Altepeter J BBranning DJeffrey EWei T CKwiat P G Thew R TO Brien J LNielsen M AWhite A G 2003 Phys Rev Lett Yao X WXue FPang W MDu J FZhou X YHan R D 2006 Chin Phys Lett Kim KSong MLee S 2005 J Kor Phys Soc

5 Subspace quantum process tomography via nuclear magnetic resonance * Yao Xi-Wei 1 Zeng Bi-Rong 2 Liu Qin 1 Mu Xiao-Yang 1 Lin Xing-Cheng 1 Yang Chun 1 Pan Jian 1 Chen Zhong 1 1 Department of PhysicsFujian Provincal Key Laboratory of Plasma and Magnetic ResonanceXiamen UniversityXiamen 2 Department of Materials Science and EngineeringXiamen UniversityXiamen China Received 31 December 2009 revised manuscript received 30 January China Abstract Experimental investigation of subspace quantum process tomography in three-spin system was implemented via nuclear magnetic resonance A quantum process was characterized by measuring a complete set of input states and corresponding outputs The method using ancillary qubit remarably reduces the number of the initial input states And the pulse sequences used in this paper have fewer J-coupling evolutions The experiment time was shortened and quantum decoherence of the system was weaened efficiently Keywords quantum computationnuclear magnetic resonanceprocess tomographysubspace PACC * Project supported by the Natural Science Foundation of Fujian ProvinceChina Grant No 2008J0219 yau@ xmu edu cn

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