Combinating random and cyclic decoupling techniques
Combinating random and cyclic decoupling techniques Combinating random and cyclic decoupling techniques
00000000000Random Decoupling [3]ˆr 5ˆr † 4ˆr 4ˆr † 3ˆr 3ˆr † 2ˆr 2ˆr † 1ˆr 1ˆr † 0ˆr 0time 5τ 4τ 3τ 2τ τ 0ˆr j ∈ {ˆ1, ˆX,Ŷ ,Ẑ}⊗n qÛ(nτ) = e −iˆr† n−1Ĥ0ˆr n−1 τ ...e −iˆr† 1Ĥ0ˆr 1τ · e −iˆr† 0Ĥ0ˆr 0 τ[3] O. Kern, G. Alber and D. L. Shepelyansky, Eur. Phys. J. D 32, 153 (2005)111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 T 0000000000011111111111 Q 0000000000011111111111 P1111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 1111111111100000000000Varenna, July 5th-15th, 2005 – p.4/7
00000000000Random Decoupling [3]ˆr 5ˆr † 4ˆr 4ˆr † 3ˆr 3ˆr † 2ˆr 2ˆr † 1ˆr 1ˆr † 0ˆr 0time 5τ 4τ 3τ 2τ τ 0ˆr j ∈ {ˆ1, ˆX,Ŷ ,Ẑ}⊗n qÛ(nτ) = e −iˆr† n−1Ĥ0ˆr n−1 τ ...e −iˆr† 1Ĥ0ˆr 1τ · e −iˆr† 0Ĥ0ˆr 0 τError bound [2]:ǫ(T) = max|Ψ 0 〉 E( 1 − |〈Ψ(T)|Ψ 0 〉| 2) ≤ O( )‖Ĥ0‖ 2 Tτ111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 T 0000000000011111111111 Q 0000000000011111111111 P1111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 1111111111100000000000[3] O. Kern, G. Alber and D. L. Shepelyansky, Eur. Phys. J. D 32, 153 (2005)[2] L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)Varenna, July 5th-15th, 2005 – p.4/7
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00000000000R<strong>and</strong>om Decoupling [3]ˆr 5ˆr † 4ˆr 4ˆr † 3ˆr 3ˆr † 2ˆr 2ˆr † 1ˆr 1ˆr † 0ˆr 0time 5τ 4τ 3τ 2τ τ 0ˆr j ∈ {ˆ1, ˆX,Ŷ ,Ẑ}⊗n qÛ(nτ) = e −iˆr† n−1Ĥ0ˆr n−1 τ ...e −iˆr† 1Ĥ0ˆr 1τ · e −iˆr† 0Ĥ0ˆr 0 τ[3] O. Kern, G. Alber <strong>and</strong> D. L. Shepelyansky, Eur. Phys. J. D 32, 153 (2005)111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 T 0000000000011111111111 Q 0000000000011111111111 P1111111111100000000000111111111110000000000011111111111000000000001111111111100000000000111111111110000000000011111111111000000000000000000000011111111111 1111111111100000000000Varenna, July 5th-15th, 2005 – p.4/7
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