Chapter 8 - Noise in Quantum Systems

Introduction

Noise is the greatest obstacle to building a scalable and reliable quantum computing device. Furthermore, all realistic quantum systems are noisy. Therefore, the objective of experimentalists trying to build quantum computing devices is the eliminate as much noise as possible. In this chapter, the objective will be to understand how to describe noise.

In Chapter 3, the Schrodinger equation was discussed as the way in which to describe quantum systems' evolution. The evolution described by Schrodinger's equation is a the evolution of a system which has been isolated from everything else, i.e., it describes a closed system. However, as just stated, realistic systems are noisy and this noise is often due to unwanted interactions with the environment. There are other noises, for example a gating operation which necessarily has a finite precision. Such noise can also be described by the representations of open quantum system evolution that are provided in this chapter. So this chapter is about noise in general.

The Operator-Sum Representation

The operator-sum representation is a method for representing open system evolution. It now goes by other names such as Kraus representation, or Kraus decomposiion. However, it originated with Sudarshan, Mathews, and Rau in 1961 (SMR) and was later taken up by Kraus and others. Kraus's name is now attached to it due to a set of lecture notes published in the early 1970's. In this section, it will likely be clear that the description in all its generality was very well (and simply) described by SMR and that is the line of argument which will be followed.

Let us consider a mapping from one density operator to another with no other restrictions.