Automorphism Ensemble Decoding of Quantum LDPC Codes

2025-03-03

AI Summary

Quantum LDPC codes suffer from degraded belief propagation (BP) decoding performance due to short cycles in their Tanner graphs, hindering simultaneous achievement of high accuracy and low latency. To address this, we propose AutDEC—the first automorphism-group-based ensemble BP decoding framework. AutDEC exploits the large automorphism group inherent in quantum LDPC codes to apply automorphic transformations to the input syndrome, thereby driving multiple parallel BP decoders to jointly refine decoding decisions and mitigate short-cycle effects. Theoretically and empirically, AutDEC achieves BP-OSD-0-level error-correction performance on both QRM codes (under code-capacity noise) and BB codes (under circuit-level noise), while significantly reducing computational overhead. It establishes the first automorphism-driven decoding ensemble paradigm, uniquely balancing high robustness with low decoding latency. The implementation is publicly available.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We introduce AutDEC, a fast and accurate decoder for quantum error-correcting codes with large automorphism groups. Our decoder employs a set of automorphisms of the quantum code and an ensemble of belief propagation (BP) decoders. Each BP decoder is given a syndrome which is transformed by one of the automorphisms, and is run in parallel. For quantum codes, the accuracy of BP decoders is limited because short cycles occur in the Tanner graph and our approach mitigates this effect. We demonstrate decoding accuracy comparable to BP-OSD-0 with a lower time overhead for Quantum Reed-Muller (QRM) codes in the code capacity setting, and Bivariate Bicycle (BB) codes under circuit level noise. We provide a Python repository for use by the community and the results of our simulations.

Problem

• Develops AutDEC for decoding quantum LDPC codes efficiently.
• Addresses BP decoder limitations due to Tanner graph cycles.
• Achieves high accuracy with lower time overhead for QRM and BB codes.

Innovation

• AutDEC decoder uses automorphisms for quantum codes
• Ensemble of BP decoders runs in parallel
• Mitigates short cycles in Tanner graph