LiftDiff: Guided Discrete Diffusion for Quantum Code Construction
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 $\mathbb{F}_2[\mathbb{Z}_\ell]$, which are then expanded into LP codes. The reverse diffusion process is guided by an energy function that evaluates quantum code...
| Authors | Yotam Peled, Eliya Nachmani |
|---|---|
| Primary category | quant-ph |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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