Quantum Error Correction & Fault Tolerance
Surface codes and qLDPC codes, below-threshold logical qubits, real-time decoding, magic-state distillation and cultivation, and resource estimates for fault tolerance.
Quantum Error Correction & Fault Tolerance: State of the Field (October 2026)
An expert briefing on quantum error correction as of late October 2026: surface, color and qLDPC codes, bosonic and erasure qubits, real-time decoding, magic-state preparation and fault-tolerant resource estimates. The main takeaway is that below-threshold error suppression has been shown on superconducting hardware, in a short neutral-atom surface-code circuit and, in a 2026 preprint, in trapped-ion color-code memories, so the bottleneck has shifted to logical gates, magic-state cost, decoding latency, correlated errors and scale. Published estimates for factoring RSA-2048 have fallen from 20 million noisy qubits (2019) to under one million (2025); 2026 preprints claim under 100,000 with qLDPC codes, and Shor's algorithm at cryptographically relevant scale on as few as 10,000 reconfigurable atoms, with runtime falling as qubits are added, all assuming hardware not yet demonstrated at scale.
Most influential
- Logical quantum processor based on reconfigurable atom arrays
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing.…
Article1,118 citationsarXiv:2312.03982doi:10.1038/s41586-023-06927-3 - Suppressing quantum errors by scaling a surface code logical qubit
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducin…
Article1,102 citationsarXiv:2207.06431doi:10.1038/s41586-022-05434-1 - Superconducting quantum circuits at the surface code threshold for fault tolerance
A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platfo…
Article1,741 citationsarXiv:1402.4848doi:10.1038/nature13171 - Quantum error correction below the surface code threshold
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two su…
Article774 citationsarXiv:2408.13687doi:10.1038/s41586-024-08449-y - How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekerå-Håstad 2017, Ekerå 2017, Ekerå 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible ph…
Article829 citationsarXiv:1905.09749doi:10.22331/q-2021-04-15-433 - Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptiona…
Article686 citationsarXiv:2112.03708doi:10.1038/s41586-022-04566-8 - State preservation by repetitive error detection in a superconducting quantum circuit
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors w…
Article918 citationsarXiv:1411.7403doi:10.1038/nature14270 - High-fidelity parallel entangling gates on a neutral-atom quantum computer
The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically recon…
Article521 citationsarXiv:2304.05420doi:10.1038/s41586-023-06481-y - Bulk locality and quantum error correction in AdS/CFT
We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether…
Article803 citationsarXiv:1411.7041doi:10.1007/jhep04(2015)163 - High-threshold and low-overhead fault-tolerant quantum memory
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high e…
Article454 citationsarXiv:2308.07915doi:10.1038/s41586-024-07107-7 - Fast universal quantum gate above the fault-tolerance threshold in silicon
Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy c…
Article472 citationsarXiv:2108.02626doi:10.1038/s41586-021-04182-y - Surface code quantum computing by lattice surgery
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally r…
Article597 citationsarXiv:1111.4022doi:10.1088/1367-2630/14/12/123011 - Realizing topologically ordered states on a quantum processor
The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error-correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an effi…
Abstract excerpt by Kevin J. Satzinger et al., CC-BY, https://doi.org/10.1126/science.abi8378; truncated.
Article426 citationsdoi:10.1126/science.abi8378 - Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information encoded in the system. Stabilizer codes are attractive solutions to this problem, as they are analogous to classical linea…
Article489 citationsarXiv:1410.6419doi:10.1038/ncomms7979 - Exponential suppression of bit or phase errors with cyclic error correction
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical info…
Article385 citationsarXiv:2102.06132doi:10.1038/s41586-021-03588-y
Newest work
- Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillatorPreprintarXiv:2610.36663
- Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum CodesPreprintarXiv:2610.36700
- Correlation-sensitive magic-state distillation from spin-squeezed neutral atomsPreprintarXiv:2610.36963
- From QCCD Trapped-Ion Hardware to Quantum Compilers: Capabilities, Architectures, and CompilationPreprintarXiv:2610.36965
- Measurement incompatibility and noiseless quantum codesPreprintarXiv:2610.37347
- Self-Correcting 3D Surface Code with Growing Local DimensionPreprintarXiv:2610.35099
- A Control Line Multiplexing Framework for Scalable Quantum ComputingPreprintarXiv:2610.35227
- Multipartite dynamics beyond bipartite entanglement equilibrationPreprintarXiv:2610.35377
- Fast and accurate rare-event simulation by Markov chain Monte Carlo for general quantum codesPreprintarXiv:2610.35498
- Geometric aspects of fault tolerancePreprintarXiv:2610.35513