Most effective decoding algorithms for real-time surface-code error correction

Identify which decoding algorithms are most effective for real-time decoding of surface-code quantum error correction under superconducting-qubit constraints, meeting stringent latency and throughput requirements for feed-forward operations at relevant code distances, and quantify the performance–flexibility trade-offs for system design.

Background

Real-time feed-forward in surface-code-based fault-tolerant quantum computation requires decoders that can process syndromes within microsecond-scale latencies to avoid stalling logic-level operations, especially on fast superconducting platforms.

Multiple decoding approaches (e.g., MWPM, Union-Find, Fusion Blossom, neural decoders) exist, but their relative effectiveness under realistic hardware noise models, latency constraints, and large-scale parallelism remains unresolved; the paper explicitly states that the most effective algorithms are not yet known.

References

Furthermore, at stage, it is not known yet what algorithms are most effective at decoding; therefore, there is a systems engineering trade-off between performance and flexibility.

— How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits  (2411.10406 - Mohseni et al., 2024) in Section: High-performance real-time decoding platform – Challenges and requirements

These observations point to a concrete open problem. The non-matchable, correlated syndrome structure of the $ZY$ code requires decoders that exploit this information without the matchability and convergence limitations of matching- and BP-based methods. The most direct route is tensor-network (TN) decoding, which was used to reach the ultrahigh thresholds of the tailored $XY$ code of Ref.. General TN decoders for 2D Pauli codes apply directly to the $ZY$ code. Learning-based approaches, such as graph-neural-network or reinforcement-learning decoders trained on the $ZY$ syndrome structure, offer a complementary, longer-term direction. Developing such a decoder and characterizing the resulting threshold improvements over MWPM, under both code-capacity and circuit-level noise, would be a valuable extension of the present work.

— Threshold Behavior of ZX and ZY Surface Codes Under Circuit-Level Biased and Crosstalk Noise  (2609.10876 - Thakur et al., 9 Sep 2026) in Section Outlook

Runtime and memory use, and their scaling with code distance, circuit width and depth, remain unquantified, with real-time decoding requiring a windowed approach to carry forward propagated information and unresolved error information consistently across window boundaries. These are left to future work.

— High-Accuracy Propagation-Assisted Local Decoding for Fast Transversal Clifford Circuits  (2610.26784 - Webber et al., 19 Oct 2026) in Section 6, Discussion and Conclusions