Introduction to Quantum Error Correction

TL;DR

This paper introduces quantum error correction, explaining the decoding and subsystems approach, describing quantum noise, and discussing fault tolerance requirements and their potential realizations in quantum technology.

Contribution

It provides an accessible overview of quantum error correction concepts, emphasizing the subsystems approach and its implications for fault-tolerant quantum computing.

Findings

Quantum noise can be classified and described effectively.

Subsystems approach offers diverse methods to meet fault tolerance.

Current quantum technology faces significant challenges for fault tolerance.

Abstract

In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied for fault tolerance. Considering the capabilities of currently available quantum technology, the requirements appear daunting. But the idea of ``subsystems'' shows that these requirements can be met in many different, and often unexpected ways.