59 10 2010 10 1000-3290 /2010 /59 10 /6837-05 ACTA PHYSICA SINICA Vol 59 No 10 October 2010 2010 Chin Phys Soc * 1 2 1 1 1 1 1 1 1 361005 2 361005 2009 12 31 2010 1 30 J PACC 036707580365 1 23 ε ρ in 1 3 ρ out ε ρ in ρ out 1 4 9 Deutsch 10 ε Shor 11 Grover 12 31 ρ out ρ out = ε ρ in = Σ V ρ in V 2 V Σ V V 13 17 = 1 V ε Liouville QED 18 21 A 2 ε ρ in = Σ χ mn A m ρ in 3 22 Hermit χ = χ mn ε 25 26 30 23 24 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 E-mail yau@ xmu edu cn
6838 59 A m ρ j = Σ β mn j ρ 6 ε CNOT23 2 3 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 23 11 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 /2 12 32 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 /2 13 14 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 2 + + 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 2 2 2 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 3 1 2 3 J π /2 12 - I 1 y / 槡 2 + 槡 2I 1 z = σ 1 π /2 x - I 2 z / 槡 2 - - 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 4 15 13 12 2 2I 1 x J 12 = 34 9 Hz J 23 = 54 0 Hz J 13 = 1 E 1 E 1-1 3 Hz 1 2 3-1 CNOT 槡 2 I2 y + I 3 z ( ) σ 1 1 E 1-2 槡 2I 1 y / 槡 2 = σ 5 16 14 ρ eq = I 1 z + I 2 z + π /2 y I 1 x + + = σ 6 J 23 π /2 I 1 x + 2 + 2I 2 z = σ 7 17 σ 1 σ 7 7 1 1 7 1 1 4 2 2 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 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 100 500 s t = 7 163 ms τ = 4 630 ms CNOT χ CNOT 2 a CNOT χ Th 2 b F = 0 84 CNOT 2 1 16 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
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10 6841 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 361005China Received 31 December 2009 revised manuscript received 30 January 2010 361005China 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 036707580365 * Project supported by the Natural Science Foundation of Fujian ProvinceChina Grant No 2008J0219 E-mail yau@ xmu edu cn