rl-list-sequential-qldpc-decoding

name	rl-list-sequential-qldpc-decoding
description	Reinforcement learning-based list sequential belief propagation decoder for QLDPC codes — extends RL-S scheduling with list-based branch exploration for improved decoding convergence.
version	1.0
created	2026-06-28
source	arxiv

RL-Based List Sequential QLDPC Decoding

Description

Methodology for decoding quantum low-density parity-check (QLDPC) codes using reinforcement learning with list-based sequential belief propagation. Extends the RL-S (reinforcement-learning-based sequential variable-node scheduling) framework with list-based search to address short cycles, degeneracy, and poor convergence of standard BP decoders.

Activation Keywords

• RL QLDPC decoder
• list sequential belief propagation
• reinforcement learning quantum error correction
• QLDPC decoding
• RL-S decoder
• 量子LDPC解码
• sequential BP scheduling

Core Problem

QLDPC codes are strong candidates for fault-tolerant quantum computation, but efficient decoding is challenging due to:

1. Short cycles in Tanner graphs causing BP oscillation
2. Degeneracy — multiple error patterns yield same syndrome
3. Poor convergence of standard belief propagation decoders

Methodology

RL-Sequential Scheduling (RL-S)

• Learned policy selects the next variable node to update at each BP iteration
• Improves convergence over random or fixed scheduling
• Policy trained via reinforcement learning on representative QLDPC codes

List-Based Extension (RL-LS)

At each scheduling step:

1. Main trajectory: Policy selects variable node, performs standard RL-S update
2. Competing branch: Softly bias post-update LLR pair toward the second-most likely Pauli symbol
3. Recompute: Update incident local BP messages for the alternative branch
4. Set: Mark visited variable node to second-best symbol
5. Rank & Prune: Candidate trajectories ranked by cumulative path metric

Cumulative Path Metric

• Tracks quality of each candidate trajectory
• Enables pruning of unpromising branches
• Balances exploration vs. computational cost

Implementation Patterns

Decoder Architecture

For each BP iteration:
  1. RL policy → select variable node v
  2. Main path: standard BP update at v
  3. List path: bias LLR → second-best Pauli symbol
  4. Recompute local messages for list branch
  5. Update cumulative path metrics
  6. Prune: keep top-K trajectories
  7. Select best trajectory for next iteration

Training Setup

• Train on representative QLDPC benchmark codes
• Depolarizing channel noise model
• Reward: successful decoding / convergence speed
• State: current syndrome, BP message configuration

Hyperparameters

• List size K: trade-off between performance and complexity
• Bias strength: how strongly to push toward second-best symbol
• Pruning threshold: when to discard candidate trajectories

Performance Characteristics

• Improves over standard BP-based decoding methods
• Extends RL-S convergence with list exploration
• Trade-off: larger list → better performance, higher complexity
• Tested on representative QLDPC benchmark codes over depolarizing channel

Applications

1. Fault-tolerant quantum computing: Reliable QLDPC decoding
2. Quantum memory: Long-term storage with error correction
3. Quantum communication: Error correction in quantum channels
4. Surface codes: Generalizable to topological codes

Related Concepts

• Belief propagation decoding
• Quantum LDPC codes
• Reinforcement learning for scheduling
• List decoding
• Syndrome-based error correction
• Degenerate quantum codes

arXiv Reference

• Paper: "Learning-Based List Sequential Belief Propagation Decoding of Quantum LDPC Codes"
• ID: 2606.20926
• URL: https://arxiv.org/abs/2606.20926
• Authors: Mohsen Moradi, Taejoon Kim, Remi A. Chou
• Published: 2026-06-18
• Categories: cs.IT, quant-ph

Notes

• Key innovation: combining learned scheduling with list exploration
• The second-best Pauli symbol exploration captures degeneracy
• Cumulative path metric enables principled pruning