Surface code error correction
Algorithms and benchmarks / Error correction (enabling)
The leading quantum error-correcting code for chips with nearest-neighbour connections: many physical qubits on a 2D grid encode one logical qubit, and repeated measurements detect errors that a classical decoder corrects in real time.
- Era
- Fault-tolerant
- Problem class
- Error correction (enabling)
- Speedup
- An enabling technique: it makes long fault-tolerant algorithms possible at a large qubit overhead.
How it works
Data qubits and measurement qubits alternate on a square grid; stabiliser measurements every cycle reveal error syndromes; increasing the code distance suppresses logical errors when physical errors are below a threshold.
Typical use cases
- The basis of most fault-tolerant resource estimates (Shor, chemistry, Hamiltonian simulation).
Related pages
Resource estimates
No resource estimate with stated assumptions was verified for this family in this release.
Demonstrations
- 2025: Distance-7 surface code memory on 101 qubits: 0.143% ± 0.003% logical error per cycle, error suppression Λ = 2.14 ± 0.02 per distance step of two, a logical lifetime 2.4 ± 0.3 times the best physical qubit, 1.1 microsecond cycles and a decoder latency of 63 microseconds on average at distance 5. (R. Acharya et al. 2025)
Hardware platforms that fit
- Superconducting qubits: A distance-7 surface code memory with 101 qubits ran below threshold with a 1.1 microsecond cycle (Acharya et al. 2025) on a processor of Google Quantum AI, whose processors are superconducting (Arute et al. 2019).
- Neutral atoms: Reconfigurable atom arrays scaled a surface code from distance 3 to 7 to improve a logical two-qubit gate (Bluvstein et al. 2023).
What you need to run it
- Classical simulation
- Stabiliser simulators (such as Stim) simulate surface-code circuits with thousands of qubits efficiently, because the circuits are Clifford.
- Noisy hardware (NISQ)
- Not applicable for this family.
- Fault-tolerant machine
- Physical error rates below the threshold, fast mid-circuit measurement and reset, and a real-time decoder; cycle times around 1 microsecond on superconducting chips.
- Annealer or analogue simulator
- Not applicable for this family.
Calculate the memory of a simulation
Where to run it in Europe
Superconducting qubits
- VLQ (Czechia; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones VLQ
- Euro-Q-Exa (Germany; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Euro-Q-Exa
- EuroQCS-Spain (Spain; Inaugurated, per the EuroHPC JU): Superconducting annealing; analogue quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones EuroQCS-Spain
- Quantum Inspire (Netherlands; In operation, per the source): Online platform with superconducting transmon QPUs, a neutral-atom emulator and simulators; a Spin-2+ electron spin QPU is listed as archived. Access: Quantum Inspire registration.
- LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
- Finnish Quantum-Computing Infrastructure (FiQCI) (Finland; In operation, per the source): Hybrid HPC and quantum computing platform: VTT Q50 (53 qubits) and Aalto Q20 (20 qubits), superconducting systems made by IQM, used through the LUMI supercomputer environment. Access: FiQCI calls for academic projects.
- Quantum Spain quantum computer at BSC-CNS (Spain; In operation, per the source): Superconducting; digital quantum computer with a 35-qubit processor, integrated into the MareNostrum 5 supercomputer. Access: Spanish Supercomputing Network (RES) quantum access. Deployment milestones Quantum Spain quantum computer at BSC-CNS
Neutral atoms
- JADE (Germany; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones JADE
- Ruby (France; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Ruby
- SOL (Italy; Planned, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones SOL
- LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
- France Hybrid HPC Quantum Initiative (HQI) platform (France; In operation, per the source): Hybrid HPC–quantum platform coupled to the Joliot-Curie supercomputer: Ruby (analogue neutral-atom system controlling 100 rubidium atoms), Lucy (12-photon photonic QPU) and Qaptiva QPU emulation. Access: GENCI eDARI resource allocation requests. Deployment milestones France Hybrid HPC Quantum Initiative (HQI) platform
The full infrastructure catalogue · The infrastructure deployment tracker
Software
European tools in the software directory
Other open-source frameworks
- Stim (Google Quantum AI (United States); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- Many physical qubits per logical qubit: Bravyi et al. (2024) put the surface code at about 3,000 physical qubits for 12 logical qubits, and the fault-tolerant estimates reach millions of physical qubits.
- Non-Clifford gates need magic states, which cost extra space and time.
- Decoding must keep up with the cycle time in real time.
In the Quantum Algorithm Zoo
No matching Zoo entry was found on 23 October 2026; the Zoo lists algorithms with a proven or conjectured speedup, not this family.
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
Named in European procurements
None of the procurement documents read for this release names it.
Sources
- A. G. Fowler, M. Mariantoni, J. M. Martinis, A. N. Cleland (2012). Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012); arXiv:1208.0928. Read: abstract page, retrieved 2026-10-23.
- R. Acharya et al. (2025). Quantum error correction below the surface code threshold. Nature 638, 920 (2025); arXiv:2408.13687. Read: abstract page, retrieved 2026-10-23.
- F. Arute et al. (2019). Quantum supremacy using a programmable superconducting processor. Nature 574, 505 (2019); supplementary information on arXiv:1910.11333. Read: arXiv page of the supplementary information, retrieved 2026-10-23.
- S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, T. J. Yoder (2024). High-threshold and low-overhead fault-tolerant quantum memory. Nature 627, 778 (2024); arXiv:2308.07915. Read: abstract page, retrieved 2026-10-23.
- D. Bluvstein et al. (2023). Logical quantum processor based on reconfigurable atom arrays. Nature (published online 2023), DOI 10.1038/s41586-023-06927-3; arXiv:2312.03982. Read: abstract page, retrieved 2026-10-23.