LiftDiff: Guided Discrete Diffusion for Quantum Code Construction
Abstract
The realization of fault-tolerant quantum computation relies on Quantum Error-Correcting Codes (QECC). Of particular interest are codes that combine a high encoding rate with sufficient distance. Existing algebraic constructions, such as lifted product (LP) codes, build a large quantum low-density parity-check (qLDPC) code from a classical base matrix. In this work we introduce LiftDiff, a generative approach to the discovery of QECC. A discrete denoising diffusion model is trained to generate base matrices over the group algebra π½2[β€β], which are then expanded into LP codes. The reverse diffusion process is guided by an energy function that evaluates quantum code properties, including girth, degree, sparsity and decoding performance, steering the sampler toward matrices that yield LP codes with favorable parameters. Our method discovers codes with parameters such as $[[169,13,11]]$, $[[143,15,9]]$, and $[[260,24,10]]$, including a $[[247,19,14]]$ code that achieves the highest kd2/n among the baselines. Moreover, several discovered codes outperform the Gross code across a broad range of the tested physical error rates under both code-capacity and circuit-level noise.
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BibTeX
@misc{peled2026liftdiff,
title = {{LiftDiff: Guided Discrete Diffusion for Quantum Code Construction}},
author = {Yotam Peled and Eliya Nachmani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25213},
eprint = {2610.25213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25213},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - LiftDiff: Guided Discrete Diffusion for Quantum Code Construction
AU - Yotam Peled
AU - Eliya Nachmani
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25213
UR - https://arxiv.org/abs/2610.25213
AB - The realization of fault-tolerant quantum computation relies on Quantum Error-Correcting Codes (QECC). Of particular interest are codes that combine a high encoding rate with sufficient distance. Existing algebraic constructions, such as lifted product (LP) codes, build a large quantum low-density parity-check (qLDPC) code from a classical base matrix. In this work we introduce LiftDiff, a generative approach to the discovery of QECC. A discrete denoising diffusion model is trained to generate base matrices over the group algebra π½_2[β€_β], which are then expanded into LP codes. The reverse diffusion process is guided by an energy function that evaluates quantum code properties, including girth, degree, sparsity and decoding performance, steering the sampler toward matrices that yield LP codes with favorable parameters. Our method discovers codes with parameters such as $[[169,13,11]]$, $[[143,15,9]]$, and $[[260,24,10]]$, including a $[[247,19,14]]$ code that achieves the highest kd^2/n among the baselines. Moreover, several discovered codes outperform the Gross code across a broad range of the tested physical error rates under both code-capacity and circuit-level noise.
ER -