PowerPoint Presentation · 10) Ry(20) (20) e le-2 le-4 le-6 le-8 le-10 le-12 le-14 le-16 LAE zero...
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Transcript of PowerPoint Presentation · 10) Ry(20) (20) e le-2 le-4 le-6 le-8 le-10 le-12 le-14 le-16 LAE zero...
Figure from: Rezakhani, Pimachev, Lidar (2010)
Landau-Zener Regime
Adiabatic Regime
E1(t)
E0(t)
(Farhi, Guttman 1999, Mackenzie, Marcotte, Paquette 2006, Cheung, Hoyer, Wiebe 2011)
+� E1(t)
E0(t) +�
E1(t)
E0(t) +⋯ 𝑈𝑈 𝑡𝑡 =
Ideal Adiabatic Evolution Error
Adiabaticity is a consequence of phase cancelation between paths that have many jumps
Ground state
Excited state
Path 1
s=0 s=1 Minimum gap
= 2𝜋𝜋 phase mile markers = important region for interference
Path 2
=0
=0
[Wiebe, Babcock 2012]
Error for H1(s) Error for H2(s)
+ = 0
Strategy
0 = sin 𝜃𝜃 2 < 𝑛𝑛 1 𝜕𝜕𝑠𝑠𝐻𝐻 𝑔𝑔 𝑠𝑠 |1 𝑔𝑔 1 >𝑔𝑔𝑔𝑔𝑝𝑝𝑔𝑔,𝑛𝑛
2 𝑔𝑔 1 𝑇𝑇𝐵𝐵− e𝑖𝑖 ∫ 𝑔𝑔𝑔𝑔𝑔𝑔 𝑔𝑔 𝑠𝑠 𝑑𝑑𝑠𝑠 𝑇𝑇𝐵𝐵
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< 𝑛𝑛 0 𝜕𝜕𝑠𝑠𝐻𝐻 𝑔𝑔 𝑠𝑠 |0 𝑔𝑔 0 >𝑔𝑔𝑔𝑔𝑝𝑝𝑔𝑔,𝑛𝑛
2 𝑔𝑔 0 𝑇𝑇𝐵𝐵
+ cos 𝜃𝜃 2 < 𝑛𝑛 1 𝜕𝜕𝑠𝑠𝐻𝐻 𝑓𝑓 𝑠𝑠 |1 𝑔𝑔 1 >𝑔𝑔𝑔𝑔𝑝𝑝𝑔𝑔,𝑛𝑛
2 𝑓𝑓 1 𝑇𝑇𝐴𝐴− e𝑖𝑖 ∫ 𝑔𝑔𝑔𝑔𝑔𝑔 𝑓𝑓 𝑠𝑠 𝑑𝑑𝑠𝑠 𝑇𝑇𝐴𝐴
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< 𝑛𝑛 0 𝜕𝜕𝑠𝑠𝐻𝐻 𝑓𝑓 𝑠𝑠 |0 𝑔𝑔 0 >𝑔𝑔𝑔𝑔𝑝𝑝𝑔𝑔,𝑛𝑛
2 𝑓𝑓 0 𝑇𝑇𝐴𝐴
For every f, a fourth order interpolatory polynomial can be found that satisfies these constraints.
s=0 1
f(s)=1
f(s)=g(s)
f(s)
g(s)
1 − Δ
s=0 1
f(s)=1
f(s)=g(s)
f(s)
g(s)
1 − Δ/2 Δ/2
