1. Analytical calculation Ideal pulse approximation
Optimal pulse sequences for qubit coupled to a general environment
Rui Li
Department of physics, fudan university, shanghai,
Dynamical decoupling through eliminating the qubit-environment coupling use pulse sequences can preserve qubit coherence [1].
Pulse sequences inevitably introduce errors, therefore, it is important to optimize pulse sequences [2,3].
The first optimal pulse sequences was found in spin-boson dephasing model [3], while it is difficult to give a optimal pulse sequences for qubit coupled to a general environment [4].
Motivation
Model
Hamiltonian
Control pulse sequences
Analytical calculation
a) Total Hamiltonian:
b) In interaction picture:
c) Non-Markovian master equation:
d) always can be written as:
e) The decaying coefficient:
Ideal pulse approximation
Discussion
We consider our theory in the case of θ=0
The case θ=0
i = even
i = odd
We can give our optimal pulse sequences:
n=2
n=4
our theory
δ1=1/4
δ2=3/4
δ1=0.095
δ2=0.345
δ3=0.655
δ4=0.905
exact results [3]
[1] L. Vilola and S. Lloyd, Phys.Rev.A 58, 2733 (1998); L.Viola, E. Knill, and S. Lloyd, Phys.Rev.Lett. 82, 2417 (1999).
[2] K. Khodjasteh and D.A. Lidar, Phys.Rev.Lett. 95, (2005); Phys.Rev.A 75, (2007).
[3] G.S. Uhrig, Phys.Rev.Lett. 98, (2007); New J.Phys. 10, (2008).
[4] G.S. Uhrig, Phy.Rev.Lett. 102, (2009); J.R. West, B.H. Fong and D.A. Lidar, Phys.Rev.Lett. 104, (2010).