fpga-quantum-decoder

name

fpga-quantum-decoder

description

Design FPGA-based neural network decoders for real-time quantum error correction (QEC) in surface code architectures. Covers hardware-software co-design, deterministic low-latency decoding under 1 microsecond, NN decoder implementation on FPGA, closed-loop feedback control, and mid-circuit Pauli-frame correction for non-Clifford logical circuits. Use when building real-time QEC systems, implementing FPGA-based decoders, designing low-latency quantum control hardware, or optimizing surface code decoding throughput for fault-tolerant quantum computing.

FPGA-Based Quantum Error Correction Decoder

Overview

Surface code QEC requires classical decoding within each QEC cycle (~1-5 μs) to prevent error accumulation. FPGA-based neural network (NN) decoders achieve deterministic sub-microsecond latency with hardware parallelism.

Key Architecture

Hardware Pipeline

Syndrome Measurements → FPGA NN Decoder → Feedback Correction → Qubit Control
     (analog)          (digital logic)     (real-time)         (microwave)

Latency Budget (from experimental results, arXiv:2605.04892)

• NN inference: 124 ns (FPGA-based)
• Full closed-loop: 550 ns
• QEC cycle: 1.25 μs
• Headroom: ~700 ns for measurement + control

NN Decoder Design

• Input: syndrome measurement history (bit strings)
• Architecture: feedforward or lightweight CNN
• Output: predicted error pattern (Pauli frame update)
• Quantization: INT8 for FPGA efficiency

Design Workflow

Step 1: NN Training

1. Generate training data via QEC simulations
2. Train NN decoder offline (Python/PyTorch)
3. Quantize to INT8 weights
4. Validate logical error rate vs minimum-weight perfect matching (MWPM)

Step 2: FPGA Implementation

1. Convert NN weights to FPGA-friendly format
2. Implement inference pipeline in HDL or HLS
3. Optimize for throughput (parallel syndrome processing)
4. Target deterministic latency < 200 ns

Step 3: Integration

1. Connect FPGA to quantum control electronics
2. Implement syndrome capture interface
3. Add feedback correction path
4. Verify closed-loop timing budget

Step 4: Mid-Circuit Feedback

For non-Clifford circuits (e.g., T-gate injection):

• Pauli-frame tracking alone is insufficient
• Real-time hardware feedback required
• Decoder must output active corrections, not just frame updates

Critical Design Parameters

Parameter	Target	Notes
Decoding latency	< 200 ns	Must fit within QEC cycle
Throughput	> 1 MHz	Keep pace with syndrome rate
Accuracy	≥ MWPM	Match or exceed classical decoder
Power	< 10 W	Cryogenic-friendly for dilution fridge
Area	< 50k LUTs	Fit on mid-range FPGA

Activation Keywords

• FPGA quantum decoder
• real-time QEC
• surface code decoder
• neural network quantum error correction
• low-latency quantum control
• hardware QEC
• FPGA NN decoder
• quantum feedback control
• Pauli-frame correction
• 实时量子纠错
• FPGA量子解码器

Related Concepts

• Surface codes (distance-3, distance-5, etc.)
• MWPM (Minimum Weight Perfect Matching)
• Union-Find decoder
• Quantum control electronics
• Cryogenic FPGA operation
• Fault-tolerant quantum computation (FTQC)
• Non-Clifford gate implementation

References

• arXiv:2605.04892 — Real-time Surface-Code Error Correction Using an FPGA-based Neural-Network Decoder