Chapter 9 - Dynamical Decoupling Controls

Introduction

In the last chapter, it was shown that a symmetry in the system-bath Hamiltonian, if present, could be used to construct states immune to noise. Under certain conditions, it is possible to create a symmetry in the evolution of a quantum system. This is done by averaging away errors though repeated use of controls which act on the system. These controls are often called "dynamical decoupling controls" and are quite generally useful controls to consider for the elimination of errors. In this chapter, a simple introduction to dynamical decoupling controls is given and some important conceptual extensions discussed.

The Single-Qubit Case

The simplest case involves the elimination of an error on a single qubit state.