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Quantum Error Correction

Turning thousands of unreliable physical qubits into a handful of trustworthy logical ones — foundational theory, experimental milestones, courses and software, and the companies building fault-tolerant hardware.

33 topics•5 categories•Updated October 2026

Foundational Theory & Tutorials

8 entries

The papers and tutorials that established quantum error correction.

01Scheme for Reducing Decoherence in Quantum Computer Memory (Shor)Peter Shor's 1995 paper showing that quantum information can be protected from errors. 02Stabilizer Codes and Quantum Error Correction (Gottesman, arXiv)Gottesman's thesis introducing the stabilizer formalism. 03An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (Gottesman)Tutorial introduction to QEC and fault tolerance. 04Fault-Tolerant Quantum Computation by Anyons (Kitaev)Kitaev's foundational paper on topological, fault-tolerant quantum computation. 05Topological Quantum Memory (Dennis et al.)Introduces the surface-code approach to quantum memory. 06Surface Codes: Towards Practical Large-Scale Quantum Computation (Fowler et al.)Standard reference on surface-code architectures. 07Quantum Computing in the NISQ Era and Beyond (Preskill)Context for why error correction matters beyond NISQ devices. 08Error Correction ZooEncyclopedia of classical and quantum error-correcting codes.

Experimental Milestones

7 entries

Experiments showing error correction working on real hardware.

09Quantum Error Correction Below the Surface Code Threshold (Nature)Google Quantum AI's experiment where larger surface codes lowered logical error. 10Quantum Error Correction Below the Surface Code Threshold (arXiv)Preprint of the Google Quantum AI result. 11Suppressing Quantum Errors by Scaling a Surface Code Logical Qubit (Nature)Google's earlier experiment scaling a surface code. 12Exponential Suppression of Bit or Phase Errors with Cyclic Error Correction (Nature)Repetition-code experiment showing exponential error suppression. 13Logical Quantum Processor Based on Reconfigurable Atom Arrays (Nature)Neutral-atom logical qubit experiment from Harvard and QuEra collaborators. 14High-Threshold and Low-Overhead Fault-Tolerant Quantum Memory (Nature)IBM's qLDPC (bivariate bicycle) codes aimed at lower overhead. 15High-Threshold and Low-Overhead Fault-Tolerant Quantum Memory (arXiv)Preprint of the IBM qLDPC paper.

Courses & Software

6 entries

Hands-on ways to learn and simulate error correction.

16Foundations of Quantum Error Correction (IBM Quantum Learning)IBM's course covering the basics of quantum error correction. 17IBM Quantum LearningFree courses on quantum computing and information. 18Quantum CountryEssays that teach quantum computing foundations. 19StimFast stabilizer-circuit simulator for designing error-correction experiments. 20PyMatchingPython package for decoding surface codes with minimum-weight matching. 21The Quantum Insider – Understanding Quantum Error CorrectionExplainer on quantum error correction.

Hardware Roadmaps & Companies

7 entries

Organisations working toward fault-tolerant quantum computers.

22Google Quantum AISuperconducting hardware and error-correction research. 23IBM Quantum Hardware and RoadmapIBM's processors and fault-tolerance roadmap. 24QuantinuumTrapped-ion hardware and error-correction research. 25QuEra ComputingNeutral-atom quantum computing. 26PsiQuantumPhotonics approach to fault-tolerant quantum computing. 27Alice & BobCat-qubit approach to hardware-efficient error correction. 28Q-CTRLError-suppression and control software.

Related Pages & Programmes

5 entries

More on this site and national programmes.

29NISQ Computing ExplainedWhat noisy intermediate-scale quantum computing means today. 30Quantum ComputingHub for quantum computing topics on this site. 31Quantum Computing VendorsDirectory of quantum hardware and cloud vendors. 32Quantum AIQuantum AI hub on this site. 33National Quantum Mission (India)India's mission on quantum computing, communication and sensing.

Frequently Asked Questions

Why do quantum computers need error correction?

Quantum gates err far more often than classical gates and qubits lose their state through decoherence, so long, useful algorithms cannot run reliably without correcting errors as they happen.

Why can't we just copy qubits as backup?

The no-cloning theorem forbids copying an unknown quantum state, and measuring a qubit to check it collapses its superposition. QEC instead spreads information across many qubits and measures parity checks, called syndromes.

What is a logical qubit?

A reliable qubit built from many noisy physical qubits using an error-correcting code. The physical-to-logical ratio depends on the code and hardware quality, and can range from tens to thousands.

What are the main code families?

Surface codes (local and hardware-friendly), stabilizer and topological codes (the theoretical framework), qLDPC codes (lower overhead but need longer-range connections) and concatenated codes (strong in theory but demanding on gate quality).

What does below threshold mean?

Below the threshold, adding more physical qubits to a code lowers the logical error rate. Google Quantum AI's 2024 experiment is cited as a convincing demonstration on a real chip.