Papers › Exact results on finite size corrections for surface codes tailored to biased noise
Exact results on finite size corrections for surface codes tailored to biased noise
Yinzi Xiao, Basudha Srivastava, Mats Granath
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The code-capacity threshold of a scalable quantum error correcting stabilizer code can be expressed as a thermodynamic phase transition of a corresponding random-bond Ising model. Here we study the XY and XZZX surface codes under phase-biased noise, pₓ=p_y=p_z/(2η), with η≥1/2, and total error rate p=pₓ+p_y+p_z. By appropriately formulating the boundary conditions, in the rotated code geometry, we find exact solutions at a special disordered point, p=(1+η⁻¹)/(2+η⁻¹)≳0.5, for arbitrary odd code distance d, where the codes reduce to one-dimensional Ising models. The total logical failure rate is given by P_f=3/4-1/4e^(-2d_Z artanh(1/2η)), where d_Z=d² and d for the two codes respectively, is the effective code distance for pure phase-flip noise. As a consequence, for code distances d≪η, and error rates near the threshold, the XZZX code is effectively equivalent to the phase-flip correcting repetition code over d qubits. The large finite size corrections for d_Z<η also make threshold extractions, from numerical calculations at moderate code distances, unreliable. We show that calculating thresholds based not only on the total logical failure rate, but also independently on the phase- and bit-flip logical failure rates, gives a more confident estimate. Using this method for the XZZX code with a tensor-network based decoder and code distances up to d≈100, we find that the thresholds converge to a single value at moderate bias (η=30, 100), at an error rate above the hashing bound.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections