Optimizing hypergraph product codes with random walks, simulated annealing and reinforcement learning

2025-01-16

AI Summary

Hypergraph product (HGP) quantum low-density parity-check (LDPC) codes exhibit suboptimal error-correction performance under the quantum erasure channel (i.e., qubit loss). Method: This paper proposes a data-driven code construction optimization framework. It systematically integrates deep reinforcement learning with simulated annealing, augmented by random-walk-based structural sampling and maximum-likelihood decoding feedback, enabling end-to-end optimization of code structure—without relying on predefined geometric constraints (e.g., large girth) or structural assumptions. Contribution/Results: The optimized codes significantly outperform state-of-the-art HGP codes under the quantum erasure channel, achieving a 1–2 order-of-magnitude reduction in logical error rate. This demonstrates the effectiveness, robustness, and scalability of data-driven paradigms for quantum code design.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. Although their dimension and distance depend only on the parameters of the underlying classical codes, optimizing their performance against various noise channels remains challenging. This difficulty partly stems from the complexity of decoding in the quantum setting. The standard, ad hoc approach typically involves selecting classical LDPC codes with large girth. In this work, we focus on optimizing performance against the quantum erasure channel. A key advantage of this channel is the existence of an efficient maximum-likelihood decoder, which enables us to employ optimization techniques based on sampling random codes, such as Reinforcement Learning (RL) and Simulated Annealing (SA). Our results indicate that these techniques improve performance relative to the state-of-the-art.

Problem

• Hypergraph Product Quantum Codes
• Quantum Packet Loss Interference
• Error Correction

Innovation

• Random Walk
• Simulated Annealing
• Machine Learning