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Quantum Error Correction: An Introductory Guide

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arxiv 1907.11157 v1 pith:V4M522PP submitted 2019-07-25 quant-ph

classification quant-ph
keywords quantumcorrectionerrorcodecodescomputingguideimplementation
verification ladder T0 review T1 audit T2 compute T3 formal
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Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Binary Gauss Stabilizers for Abelian Lattice Gauge Theories

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Binary Gauss stabilizers provide a non-Pauli stabilizer description of the physical subspace of Z_{2^η} lattice gauge theories, enabling bit-flip error correction and gauge fixing from gauge constraints alone.

  2. Celestial Quantum Error Correction II: From Qudits to Celestial CFT

    hep-th 2024-12 conditional novelty 6.0 of 10

    A GKP-style qudit code on a chain embedded in Klein spacetime is shown to flow, in the continuum limit, to a celestial CFT whose logical states carry quantized supertranslation hair protected from soft graviton errors.

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