Introduction

discover which error has occurred. Second, the no-cloning theorem prevents

us from creating redundant quantum information by cloning a qubit. Also,

one cannot think of copying an output before measuring it.

Nevertheless, as we will see in this section, it is possible to correct qubits for

errors in an intrinsic manner without destroying the information they carry. It

also turns out that the whole continuum of possible errors can be represented

by a finite set of discrete errors. In short, quantum error correction is possible

and efficiently implementable. We will study the basic principles of how this

works in the somewhat artificial but simple context of single-qubit errors