coset-ensemble-decoder-qec

name	coset-ensemble-decoder-qec
description	Coset Ensemble Decoder for Quantum Error Correction with Algorithm-Hardware Co-Design methodology. Ensemble forest exploration exploiting logically equivalent cosets to improve Union-Find decoding, with domain-specific FPGA architecture reducing LUT consumption 8.2x. Use when: (1) designing QEC decoders for fault-tolerant quantum computing, (2) optimizing accuracy-latency trade-offs in real-time syndrome decoding, (3) implementing hardware-efficient QEC decoders on FPGA, (4) ensemble decoding approaches for surface codes. Activation: coset ensemble decoding, QEC decoder, Union-Find decoder, syndrome decoding, quantum error correction, FPGA decoder, algorithm-hardware co-design, fault-tolerant decoding, surface code decoder, real-time QEC, min-weight perfect matching, coset-level maximum-likelihood
metadata	{"arxiv_id":"2606.11076","published":"2026-06-09","authors":"IM Seon et al."}

Context

Fault-tolerant quantum computation requires real-time QEC decoding that simultaneously delivers high logical accuracy and ultra-low latency. Traditional decoders (MWPM, Union-Find) face an accuracy-latency trade-off. This paper introduces coset ensemble decoding — an algorithm-hardware co-design that improves UF decoding by exploiting logically equivalent cosets, with an FPGA architecture that reduces resource consumption 8.2x.

Core Methodology

1. Coset Ensemble Decoding (Algorithm)

• Coset Exploitation: Multiple logically equivalent cosets produce the same syndrome — enumerate candidates across cosets rather than selecting single minimum-weight matching
• Ensemble Forest Exploration: Generate multiple coset-consistent UF forest candidates, aggregate to approximate coset-level maximum-likelihood decoding
• Reverse-Order Elimination: Reduce computational complexity by processing elimination in reverse order
• Lossless Graph Compression: Compress syndrome graph without accuracy loss to reduce memory footprint

2. Domain-Specific FPGA Architecture (Hardware)

• Temporal Resource Reuse: Avoids code-distance-proportional resource growth via time-multiplexed processing units
• Multi-Bank Memory Hashing: Mitigates pipeline stalls under concurrent syndrome access patterns
• Hierarchical ID Mapping: Resolves memory conflicts in highly concurrent syndrome extraction

3. Accuracy-Latency Trade-Off

• Tunable candidate number parameter: users adjust decoding performance vs. latency based on workload requirements
• Under circuit-level depolarizing noise: better accuracy-latency than MWPM and UF baselines
• 8.2x reduction in FPGA LUT consumption vs. reported UF-based decoder resources

Implementation Steps

1. Implement Union-Find decoder as base algorithm
2. Extend to enumerate logically equivalent cosets for each syndrome
3. Build ensemble forest exploration: generate N coset-consistent candidates
4. Implement aggregation mechanism for coset-level ML approximation
5. Apply reverse-order elimination for computational efficiency
6. Apply lossless graph compression for memory reduction
7. Design FPGA architecture with temporal resource reuse
8. Implement multi-bank memory hashing and hierarchical ID mapping
9. Benchmark under circuit-level depolarizing noise model
10. Tune candidate number parameter for target accuracy-latency point

Key Results (arXiv:2606.11076)

• LUT reduction: 8.2x vs. prior UF-based FPGA decoder resources
• Accuracy: Better than MWPM and UF baselines under circuit-level noise
• Tunability: Candidate number provides flexible performance knob
• Availability: Implementation at github.com/IMSeonL/coset-ensemble-decoder
• Noise model: Circuit-level depolarizing noise

Pitfalls

• Candidate Number Scaling: Increasing candidate count improves accuracy but increases latency — the trade-off must be calibrated for target fault-tolerant workload
• Code Distance Scaling: Temporal resource reuse may become bottleneck at very large code distances (d > 20) where sequential processing dominates
• Noise Model Specificity: Results demonstrated under circuit-level depolarizing noise — verify for biased noise, leakage, or crosstalk models
• Hardware-Specific Optimizations: Multi-bank memory hashing and hierarchical ID mapping are FPGA-specific — ASIC or GPU implementations require different approaches
• Coset Enumeration Completeness: The ensemble approach approximates coset-level ML; full enumeration may be intractable for large codes

Verification

1. Implement coset ensemble decoder in Python/C++ for simulation
2. Compare logical error rate vs. standard UF decoder at same code distance
3. Verify accuracy improvement under circuit-level depolarizing noise
4. Synthesize FPGA design and measure LUT/BRAM/DSP utilization
5. Confirm 8.2x LUT reduction vs. baseline UF decoder
6. Measure decoding latency vs. candidate number parameter
7. Validate tunable accuracy-latency trade-off curve

Code Reference

Implementation available at: https://github.com/IMSeonL/coset-ensemble-decoder