Optimal dynamical decoupling sequence for the Ohmic spectrum

Yu Pan,Wei Cui,Zai-Rong Xi

doi:10.1103/physreva.81.022309

Abstract

We investigate the optimal dynamical decoupling sequence for a qubit coupled to an ohmic environment. By analytically computing the derivatives of the decoherence function, the optimal pulse locations are found to satisfy a set of nonlinear equations which can be easily solved. These equations incorporates the environment information such as high-energy (UV) cutoff frequency \omega_c, giving a complete description of the decoupling process. The solutions explain previous experimental and theoretical results of locally optimized dynamical decoupling (LODD) sequence in high-frequency dominated environment, which were obtained by purely numerical computation and experimental feedback. As shown in numerical comparison, these solutions outperform the Uhrig dynamical decoupling (UDD) sequence by one or more orders of magnitude in the ohmic case.

Highlights

Suppressing decoherence is one of the fundamental issues in the field of quantum information processing
We start our simulation by solving the non-linear equations (13) and evaluate the decoherence function with these solutions
Computing solutions to (13) for different ωc, we find that the optimal pulse sequences behave differently

Summary

INTRODUCTION

Suppressing decoherence is one of the fundamental issues in the field of quantum information processing. LODD, along with its simplified version optimized noise-filtration dynamic decoupling (OFDD) [15], generates the decoupling sequence by directly optimizing the decoherence function using numeric methods as well as experimental feedback. S. Uhrig has made an analytical progress in optimizing the decoherence function for power law spectrum (PLODD) [13]. Optimal performance pulse sequence is found analytically which entirely differs from the UDD sequence in such environment. We call this kind of optimal sequence HLODD (LODD for ohmic spectrum) for short.

OPTIMIZATION OF THE DECOHERENCE FUNCTION

DERIVATION OF OPTIMAL PULSE SEQUENCE

NUMERICAL RESULTS

CONCLUSIONS