fpga-quantum-error-decoder

name

fpga-quantum-error-decoder

description

FPGA-based real-time quantum error correction decoding architecture. Combines hardware-integrated NN decoders on FPGA with superconducting quantum processors for low-latency closed-loop QEC. Use when: (1) Designing real-time QEC control systems, (2) Implementing FPGA-based syndrome decoders, (3) Building low-latency feedback loops for fault-tolerant quantum computing, (4) Analyzing closed-loop latency budgets for QEC cycles, (5) Implementing mid-circuit Pauli-frame corrections in non-Clifford logical circuits. Trigger: FPGA QEC decoder, real-time quantum error correction, low-latency syndrome decoding, hardware integrated QEC, surface code FPGA, closed-loop quantum feedback.

FPGA-Based Real-Time Quantum Error Decoder

Hardware-integrated control architecture for real-time surface-code QEC using FPGA-based neural network decoders, achieving deterministic closed-loop latency of 550 ns (124 ns NN decoding) within a 1.25 μs QEC cycle.

Core Architecture

Quantum Processor → Syndrome Measurement → FPGA Controller → NN Decoder → Feedback Correction
     (superconducting)    (repeated)      (Xilinx/Intel)   (124 ns)    (within 1.25 μs)

Key Metrics (from arXiv:2605.04892)

Component	Latency	Description
NN Decoding	124 ns	FPGA-based neural network inference
Total Closed-Loop	550 ns	End-to-end syndrome to correction
QEC Cycle	1.25 μs	Full error correction cycle period
Code Distance	d=3	Surface code demonstration

Hardware Design Principles

1. Deterministic Latency: Fixed-latency FPGA pipelines avoid timing jitter
2. On-Chip NN Inference: Neural network weights stored in FPGA BRAM/LUTs
3. Closed-Loop Feedback: Decoder output directly drives quantum control pulses
4. Mid-Circuit Correction: Supports Pauli-frame updates during logical operations

Implementation Workflow

Step 1: Neural Network Quantization for FPGA

# Quantize trained decoder to FPGA-friendly precision
import torch

# Original: float32 trained model
model = load_trained_decoder()  # CNN/MLP for syndrome decoding

# Quantize to INT8 for FPGA deployment
model_int8 = torch.quantization.quantize_dynamic(
    model, {torch.nn.Linear, torch.nn.Conv2d}, dtype=torch.qint8
)

# Export weights for FPGA synthesis
torch.onnx.export(model_int8, dummy_syndrome, "decoder_int8.onnx")

Step 2: FPGA Pipeline Design

Input Layer (syndrome bits) → [FPGA registers]
    ↓
Convolution Layer → [DSP slices + BRAM for weights]
    ↓
Activation (ReLU) → [LUT-based lookup]
    ↓
Output Layer (correction bits) → [Pipeline registers]
    ↓
Control Signal → Quantum processor feedback

Latency Budget Breakdown:

• Syndrome readout: ~100 ns
• NN inference (INT8): 124 ns
• Correction computation: ~50 ns
• Control signal routing: ~100 ns
• Total: 550 ns

Step 3: QEC Cycle Integration

# Pseudocode for QEC cycle management
def qec_cycle(fpga_controller):
    # 1. Trigger syndrome measurement
    syndromes = measure_stabilizers()  # X and Z stabilizers
    
    # 2. Send to FPGA decoder (550 ns round-trip)
    corrections = fpga_controller.decode(syndromes)
    
    # 3. Apply feedback within QEC cycle
    if corrections.needs_feedback:
        apply_physical_correction(corrections)
    else:
        update_pauli_frame(corrections)
    
    # Must complete within 1.25 μs to prevent error accumulation
    assert elapsed_time() < 1250  # ns

Critical Design Considerations

Latency vs Accuracy Tradeoff

Decoder Latency	Logical Error Rate	Use Case
< 200 ns	~0.1% degradation	Real-time feedback
< 1 μs	~0.01% degradation	Near-real-time
> 10 μs	Baseline (offline)	Post-processing

Scaling to Larger Distances

For distance-5 and distance-7 surface codes:

• Syndrome data size grows as d²
• NN model size grows proportionally
• FPGA resource utilization: LUTs, DSPs, BRAM
• Pipeline parallelism is key: decode multiple syndrome patches concurrently

Mid-Circuit vs Pauli-Frame Correction

• Pauli-frame updating: Software-only, zero latency, works for Clifford circuits
• Mid-circuit feedback: Required for non-Clifford gates (T-gates, magic state distillation)
• FPGA decoder enables mid-circuit correction when Pauli-frame alone is insufficient

Error Model Adaptation

The FPGA-based NN decoder adapts to varying error conditions:

Training: Offline NN training with diverse noise models
Deployment: FPGA inference adapts to real-time error statistics
Adaptation: Periodic model updates based on observed syndrome patterns

Robustness Features

1. Error condition variation: Maintains performance across different physical error rates
2. Calibration drift: Retraining triggers when logical error rate exceeds threshold
3. Crosstalk compensation: NN naturally learns spatial error correlations

Comparison with Traditional Decoders

Feature	MWPM	BP	FPGA-NN Decoder
Latency	ms-scale	μs-scale	124 ns
Hardware	CPU/GPU	CPU/FPGA	FPGA (dedicated)
Adaptability	Fixed model	Iterative	Learned patterns
Circuit-level noise	Requires modification	Limited	Native support
Real-time feedback	No	Marginal	Yes

Resources

• arXiv:2605.04892: "Real-time Surface-Code Error Correction Using an FPGA-based Neural-Network Decoder"
• arXiv:2605.04459: "Triage: Adaptive Parallel Window Decoding Scheduler"
• Related skill: neural-decoder-quantum-error-correction (algorithm-level)
• Related skill: quantum-fault-tolerance-verification (verification methods)