Threshold theory and numerical validation for just-in-time ILP decoding

Construct and numerically study a just-in-time integer linear programming decoder for practical non-Abelian topological orders, and prove an associated error-correction threshold in the presence of anyon-syndrome measurement errors.

Background

The paper formulates a spacetime binary linear programming decoder for arbitrary topological orders with noisy syndrome measurements and proposes a just-in-time protocol that corrects sufficiently old clusters of defects. The protocol is presented as a proof-of-principle algorithm rather than a fully validated practical decoder.

The authors explain that a threshold proof would require controlling whether correction operations spread identified clusters temporally into higher levels of a hierarchical cluster structure. They leave the explicit construction, numerical study, and threshold proof for future work, making this an unresolved problem directly concerning the practical reliability of continuous non-Abelian error correction.