Defect-Adaptive Lattice Surgery on Irregular Boundary Surface-Code Patches

Abstract:Defect-adaptive surface-code methods construct valid logical patches on imperfect hardware, but fault-tolerant computation also requires certifying that requested logical operations remain executable on the resulting irregular geometries. We address this problem for lattice-surgery merges whose interfaces intersect deformed boundaries, unavailable checks, or gauge-inferred operators. Our compiler constructs an admissible seam-measurement set whose elements associate effective seam supports with raw-outcome selectors and schedule metadata. A GF(2) row-space test then determines whether the requested joint parity is realizable modulo pre-merge stabilizer constraints, returning either an explicit parity-extraction rule or a dual witness of non-realizability within the evaluated set. Paired ablations isolate the contribution of the proposed measurement-set construction rules. We further apply the test to configurations generated by Snakes and Ladders (SnL) on 15,000 clustered boundary-defect maps. Adding the proposed boundary-reconstruction rows increases the certification rate from 61.88\% to 62.79\%, with the gain concentrated in strongly clustered regimes. The framework therefore provides a compiler step that separates defect-adaptive patch construction from the certification and extraction of lattice-surgery parity measurements.

arXiv:2604.25524 [quant-ph]

(or arXiv:2604.25524v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.25524 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.