{
  "id": "1302.3428",
  "version": "v7",
  "published": "2013-02-14T15:20:12.000Z",
  "updated": "2015-04-10T07:16:30.000Z",
  "title": "Quantum Error Correction for Quantum Memories",
  "authors": [
    "Barbara M. Terhal"
  ],
  "comment": "Final version: 47 pages, 17 Figs, 311 references",
  "journal": "Rev. Mod. Phys. 87, 307 (2015)",
  "doi": "10.1103/RevModPhys.87.307",
  "categories": [
    "quant-ph"
  ],
  "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.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-09T14:02:20.000Z",
      "abstract": "This is a pedagogical review of the formalism of qubit stabilizer codes and their possible use in protecting quantum information. We discuss several codes of particular physical interest, e.g. encoding a qubit in an oscillator, 2D topological error correction and 2D subsystem codes. The emphasis in this review is on the use of such codes as a quantum memory.",
      "comment": "v3 has 31 pages (16 Figs) and has substantially more material and references than v2. Submitted to Rev. Mod. Phys. Corrections, comments or criticism is welcome: please email to qmemoryreview@gmail.com",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-11-28T21:08:35.000Z",
      "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 the Clifford group and the route towards fault-tolerant universal quantum computation. The second part of the review is focused on a 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.",
      "comment": "v4 has 46 pages (17 Figs) and has substantially more material and references than v3. Under consideration at Rev. Mod. Phys. Corrections, comments or criticism are welcome: please email to qmemoryreview@gmail.com",
      "journal": null,
      "doi": null
    },
    {
      "version": "v7",
      "updated": "2015-04-10T07:16:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum error correction",
      "quantum memory",
      "qubit stabilizer codes",
      "2d subsystem codes",
      "2d topological error correction"
    ],
    "tags": [
      "journal article",
      "review article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Rev. Mod. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3428T"
    }
  }
}