# Distance Prediction for Quantum Codes

arXiv: https://arxiv.org/abs/2610.18130 · HTML: https://mlsanity.com/paper/2610.18130/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 71 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/1810.07207/) (2018)
- [Denoising Diffusion Error Correction Codes](https://mlsanity.com/paper/2209.13533/) (2022)
- [CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes](https://mlsanity.com/paper/2405.01033/) (2024)
- [Advantages of versatile neural-network decoding for topological codes](https://mlsanity.com/paper/1802.08680/) (2018)
- [A scalable and real-time neural decoder for topological quantum codes](https://mlsanity.com/paper/2512.07737/) (2025)
- [Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search](https://mlsanity.com/paper/2606.02418/) (2026)
- [OmniQEC: discovering practical quantum error-correcting codes by an AI scientist](https://mlsanity.com/paper/2607.25865/) (2026)
- [Multi-agent discovery of practical quantum LDPC codes](https://mlsanity.com/paper/2608.08996/) (2026)
- [Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes](https://mlsanity.com/paper/2408.10743/) (2024)
- [Neural Minimum Weight Perfect Matching for Quantum Error Codes](https://mlsanity.com/paper/2601.00242/) (2026)
- [SAT, MaxSAT, and SMT for QLDPC Distance Computation: A Large-Scale Empirical Study](https://mlsanity.com/paper/2606.12445/) (2026)

## Abstract (arXiv)

The distance of a quantum code is a fundamental metric that dictates its error-correction capability. While quantum low-density parity-check (qLDPC) families such as Bivariate Bicycle (BB) codes offer a promising pathway to low-overhead fault-tolerant quantum computing, computing their distance is challenging. Current exact solvers and even search heuristics that provide a distance upper bound suffer from severe computational bottlenecks, restricting the discovery of optimal codes. In this paper, we construct a dataset of BB codes with corresponding distance upper bounds obtained through high-budget heuristic searches. We introduce BB-Net, an attention-based neural network architecture for predicting the distance of BB codes. It achieves 96.39% accuracy on the reference distances in the test set, compared with 94.86% for state-of-the-art heuristics with a budget of up to 104 times more computational runtime. On a subset with certified exact distances, BB-Net achieves 98.94%. By relieving the distance-calculation bottleneck, BB-Net enables faster screening of large code spaces, particularly in ML-driven search pipelines, and thereby can accelerate the discovery of novel quantum error-correcting codes, an important capability for advancing scalable fault-tolerant quantum computing. Our code is publicly available: https://github.com/NadavSc/BBNet