Quantum Error Correction for Quantum Memories

TL;DR

This paper reviews quantum error correction methods, especially stabilizer codes and surface codes, highlighting their theoretical foundations, practical challenges, and potential for fault-tolerant quantum memory and computation.

Contribution

It provides a comprehensive overview of stabilizer codes, fault-tolerance, and topological codes, emphasizing their role in developing reliable quantum memories and scalable quantum computers.

Findings

Discussion of quantum error correction conditions and noise thresholds.

Analysis of surface code architecture and decoding complexity.

Exploration of passive and self-correcting quantum memories.

Abstract

Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory. We review the theory of fault-tolerance and quantum error-correction, discuss examples of various codes and code constructions, the general quantum error correction conditions, the noise threshold, the special role played by Clifford gates and the route towards fault-tolerant universal quantum computation. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular the surface code architecture. We discuss the complexity of decoding and the notion of passive or self-correcting quantum memories. The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies.