Chapter 11 - Hybrid Methods of Quantum Error Prevention

Introduction

One of the first proposals for combining error prevention methods was due to D.A. Lidar, D. Bacon, K.B. Whaley, Phys. Rev. Lett. 82 (1999) 4556-4559. However, a great deal more work has been done since that time to provide methods for combining these seemingly very different methods of error prevention -- quantum error correcting codes, decoherence-free/noiseless subsystems, and dynamical decoupling controls. In this chapter a few general guiding principles are provided for combining these error prevention methods into hybrid methods of error prevention. Beyond that, a few very specific examples are given which are promising for error prevention and control of quantum systems for quantum information processing.

General Principles for Combining Error Prevention Methods

Perhaps it is not surprising that group theory can be used to describe the error prevention methods and their combinations. In the case of DFS/NS, it is clear that there is a symmetry involved in the process of identifying and utilizing the method. The stabilizer formalism leads to the connection between both the classical error correction, where group theory is used, and also the Pauli group. Dynamical decoupling can be seen as averaging away errors, but averaging is creating a symmetry as seen in the group-theoretical description of the dynamical decoupling condition.