A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+

1. Problem Statement

Quantum Error Correction (QEC) is transitioning from purely algorithmic research to an architecture phase where hardware data structures, logical encoding, and decoder policies must be evaluated as a coupled system. A critical bottleneck exists in benchmarking decoders for hybrid Continuous-Variable (CV) and Discrete-Variable (DV) systems (specifically photonic GKP-based architectures):

• Heterogeneous Inputs: Hardware providers (e.g., Xanadu) expose native outputs in diverse formats (shot records, switch traces, count summaries, matrix structures).
• Ingestion Drift: Without a fixed interface, differences observed between decoders (e.g., MWPM vs. Belief Propagation) may stem from how data is parsed or normalized ("ingestion drift") rather than true policy differences.
• Lack of Standardization: There is no unified execution stack that allows for the deterministic replay of hardware-derived syndrome data across multiple decoder engines to isolate policy effects from input structure effects.

2. Methodology: The LiDMaS+ Architecture

The authors propose LiDMaS+, a unified hardware-to-logical-to-decoder execution stack designed to decouple input ingestion from decoder logic.

A. Unified IO Contract

The core innovation is a line-oriented request/response contract that normalizes heterogeneous provider data into a single schema:

• Request Line: Contains code ID, round index, qubit count, a list of syndrome events (index, time, type), noise priors (sigma, gate/measurement rates), and metadata (provider, backend, source format).
• Response Line: Contains the correction (qubit flips, decoder label, confidence) and diagnostics (syndrome counts, warning flags).
• Provider Integration: A narrow adapter layer converts raw provider data (e.g., Xanadu's Aurora, QCA, GKP datasets) into this standard format, isolating vendor-specific logic from the shared decoder replay logic.

B. Deterministic Replay Pipeline

The system executes a two-stage process:

1. Conversion: Normalizes raw hardware data into the standard request stream, ensuring consistent noise priors and metadata.
2. Replay: Executes the identical request stream across multiple decoders (MWPM, Union-Find, Belief Propagation, and Neural-MWPM) under fixed controls.

• Validation: The pipeline checks for parse errors, line-count consistency, decoder-name mismatches, and diagnostic flags (e.g., "no-syndrome" warnings).
• Reproducibility: The system generates SHA-256 fingerprints for all artifacts, ensuring that re-running the analysis yields identical results.

C. Case Study & Datasets

The study utilizes Xanadu public datasets as the primary integration case:

• Fixture Data: 108 lines covering four input families (Job-style, Aurora switch traces, GKP count summaries, QCA shot matrices).
• Real Data Slices: 4,000 lines drawn from public datasets (Aurora batch 0, QCA Fig 3b).
• Control: A synthetic "held-out" dataset with matched syndrome sparsity was used to distinguish between photonic-provider specific effects and general decoder behavior.

3. Key Contributions

1. Unified Architecture: A hardware-agnostic execution stack that preserves event, noise, and provenance semantics across heterogeneous sources.
2. Decoupled Evaluation: The ability to separate input-structure effects (inherited from hardware) from correction-policy effects (introduced by the decoder).
3. Deterministic Benchmarking: A framework enabling auditable, reproducible regeneration of matrix summaries and comparative figures via SHA-256 verification.
4. Empirical Decoder Signatures: Quantitative evidence that decoder performance is regime-dependent, specifically regarding the trade-off between intervention volume and residual syndrome burden.

4. Key Results

The study evaluated four decoders: MWPM (Minimum Weight Perfect Matching), UF (Union-Find), BP (Belief Propagation), and Neural-MWPM.

A. Interface Correctness

• 100% Replay Integrity: 108/108 fixture lines and 4,000/4,000 real-data lines were processed with zero parse errors, zero decoder-name mismatches, and a response ratio of exactly 1.0.
• Stability: Input diagnostics (e.g., "no-syndrome" warning rates) remained invariant across decoders, confirming that the conversion layer did not alter input sparsity semantics.

B. Decoder Behavior & Trade-offs

Under matched inputs, decoder behaviors were clearly separable and regime-dependent:

• Intervention vs. Residual Burden:
  • Belief Propagation (BP): Consistently intervention-conservative. It proposed fewer flips (lower average flip count) but left a higher residual syndrome burden.
    • Fixture Data: BP reduced weighted correction volume by 48.6% vs. MWPM.
    • Real Data: BP reduced weighted correction volume by 50.4% vs. MWPM and 57.1% vs. UF.
  • MWPM/UF/Neural-MWPM: More intervention-aggressive. They cleared more syndrome (higher satisfaction rates) but at the cost of higher flip counts.
• Regime Dependence:
  • In sparse regimes (e.g., Aurora real slices), BP's reduction in flip count was dramatic (~78.7% vs. MWPM).
  • In denser regimes (e.g., QCA slices), the gap narrowed but BP remained the most conservative.
• Syndrome Satisfaction: MWPM-family decoders achieved a syndrome-satisfaction rate of 1.000, while BP achieved ~0.777 (weighted), confirming that BP's lower flip count correlates with higher residual error in these specific runs.

C. Robustness

• Engine-Swap Invariance: Swapping decoders via configuration did not affect request counts or warning rates, proving the "same input, swappable engine" capability.
• Sparsity Sensitivity: The separation between decoders was amplified in sparse input windows, suggesting that decoder choice is critical when syndrome density is low.

5. Significance and Implications

• Architectural Shift: The paper establishes that decoder selection is not a "one-size-fits-all" decision but a policy surface defined by the operating regime (sparsity, noise structure).
• Deployment Strategy: For photonic GKP-oriented programs, static decoder deployment is likely suboptimal. The results advocate for regime-aware adaptive or hybrid strategies (e.g., using conservative BP in low-risk sparse windows and aggressive MWPM when residual control is critical).
• Benchmarking Standard: LiDMaS+ provides the necessary substrate to move QEC benchmarking from offline algorithmic exercises to hardware-facing architecture validation. It allows researchers to attribute performance differences to policy rather than data ingestion artifacts.
• Future Roadmap: The architecture is designed to scale to additional providers (e.g., Google, Quandela) and larger datasets, supporting the transition toward fault-tolerant hybrid CV-DV quantum computing.

In summary, this work provides the first unified, deterministic framework for comparing QEC decoders across hybrid CV/DV hardware, revealing that the choice of decoder is a fundamental trade-off between intervention cost and residual error, heavily influenced by the sparsity of the hardware-generated syndrome stream.