Quantum low-density parity-check (qLDPC) codes
Algorithms and benchmarks / Error correction (enabling)
Codes that encode several logical qubits in one block with far fewer physical qubits than the surface code, at the price of more complex connections between qubits.
- Era
- Fault-tolerant
- Problem class
- Error correction (enabling)
- Speedup
- Lower overhead: about ten times fewer physical qubits than the surface code for the same protection in the cited estimate.
How it works
Each parity check involves only a few qubits (low density) and one block encodes many logical qubits; syndrome cycles measure all checks and a decoder corrects errors.
Typical use cases
- Quantum memories and future fault-tolerant processors with fewer qubits.
Resource estimates
Figures exactly as stated by their authors, with their assumptions. They are estimates under those assumptions, not forecasts, and they tend to fall as methods improve.
| Quantity | Value as stated |
|---|---|
| Physical qubits | 288 |
| Syndrome cycles preserved | nearly one million |
| Surface code equivalent | about 3,000 physical qubits |
Assumptions: Physical error rate 0.1% in the standard circuit-based noise model, with an error threshold of 0.8%; syndrome measurement with a depth-7 circuit of CNOT gates and one ancilla per data qubit.
Source: S. Bravyi et al. 2024, Nature 627, 778 (2024); arXiv:2308.07915
Demonstrations
- 2023: Up to 48 logical qubits entangled with 228 logical two-qubit gates and 48 logical CCZ gates on up to 280 physical qubits of a reconfigurable atom array. (D. Bluvstein et al. 2023)
Hardware platforms that fit
- Neutral atoms: Reconfigurable atom arrays can move qubits to make non-local connections; they ran logical circuits with surface, colour and [[8,3,2]] codes (Bluvstein et al. 2023).
What you need to run it
- Classical simulation
- Stabiliser simulation and decoder studies on workstations or HPC nodes.
- Noisy hardware (NISQ)
- Not applicable for this family.
- Fault-tolerant machine
- Physical error rates around 0.1% and fast decoders; for 12 logical qubits, 288 physical qubits in the cited estimate.
- Annealer or analogue simulator
- Not applicable for this family.
Calculate the memory of a simulation
Where to run it in Europe
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
- The cited result is a memory that stores logical qubits; computing on them needs further constructions.
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
- 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.