Quantum error correction for quantum memories

Research output: Contribution to journalReview articleScientificpeer-review

262 Citations (Scopus)

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 the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory are considered. The theory of fault tolerance and quantum error correction is reviewed, and 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 toward fault-tolerant universal quantum computation are discussed. 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. The complexity of decoding and the notion of passive or self-correcting quantum memories are discussed. The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies.

Original languageEnglish
Article number307
Pages (from-to)307-346
Number of pages40
JournalReviews of Modern Physics
Volume87
Issue number2
DOIs
Publication statusPublished - 2015
Externally publishedYes

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