lottery-bp-decoding

name

lottery-bp-decoding

description

Lottery BP methodology for scalable quantum error correction decoding. Introduces randomness during belief propagation decoding to improve accuracy by 2-8 orders of magnitude for topological codes (surface, toric, BB codes). Use when: quantum error correction, qLDPC decoding, scalable quantum decoders, belief propagation for quantum codes, syndrome processing, PolyQec architecture, or when building fault-tolerant quantum computing systems requiring real-time decoding.

Lottery BP: Scalable Quantum Error Decoding

Core Innovation

Standard Belief Propagation (BP) decoders for quantum LDPC codes suffer from error degeneracy — multiple equivalent error patterns produce identical syndromes, causing BP to fail. Lottery BP breaks this symmetry by introducing controlled randomness during decoding iterations.

Key Concepts

1. Lottery BP Decoder

• Add randomness to variable node updates during BP message passing
• Each decode attempt uses different random seeds
• Multiple independent attempts → select lowest-weight solution
• Improves accuracy by 2-8 orders of magnitude over standard BP for topological codes

2. Syndrome Vote (Pre-processing)

• Compress multiple rounds of measurement syndromes into a single syndrome
• Majority voting across temporal syndrome rounds
• Increases latency margin and mitigates decoder backlog
• Essential for multi-round measurement error handling

3. PolyQec Architecture

Two-level decoding hierarchy:

• Local decoder: Lottery BP (fast, high accuracy for most errors)
• Global decoder: Ordered Statistics Decoding (OSD) (slow, used only when BP fails)
• Lottery BP's improved local accuracy reduces OSD invocations by 3-5 orders of magnitude

4. Syndrilla Simulator

• PyTorch-based modular decoding simulation pipeline