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Paper 1

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

GunSik Min, Yujin Kang, Jun Heo

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.25524

arXiv

2604.25524

Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular geometries. We formulate the seam-boundary defect problem: how to perform a lattice-surgery merge when the intended seam intersects deformed boundaries, disabled checks, and gauge-inferred super-stabilizers. We introduce a defect-adaptive lattice-surgery method that reconstructs the target joint logical parity from the seam-related measurements available on the irregular merged patch, together with constraints inherited from the separated pre-merge code space. The reconstruction is expressed as a compact GF(2) binary-support synthesis problem. If the requested parity is realizable, the solution gives an executable parity-extraction rule over raw, schedule-tagged gauge outcomes; otherwise, it certifies a parity-synthesis failure rather than conflat ing it with patch invalidity. The framework accommodates boundary data-qubit defects, seam-check ancilla defects, and gauge-inferred seam super-checks within a single synthesis layer. Circuit-level samples of the synthesized merge operation show improved compile yield, preserved effective dis tance, and only modest success-conditioned logical-error overhead relative to the defect-free merge reference; an explicit ZZ-merge sampling check confirms the expected transposed-geometry behav ior under the same success-conditioned observable construction. More broadly, the results identify certified parity synthesis as a compilation layer between defect-adaptive patch construction and executable fault-tolerant logical operations on imperfect surface-code hardware.

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Paper 2

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Yijia Xu, Yixu Wang, En-Jui Kuo, Victor V. Albert

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04573

arXiv

2209.04573

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

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