Symmetry-Aware INT4 Quantized GNN Decoder: ASIC Synthesis and Low-Latency Surface Code Architecture

Real-time quantum error correction for superconducting processors requires decoding streaming syndrome data within microsecond cycle intervals (T_cycle ≈ 1.1 μs). Classical minimum-weight perfect matching executed on host processors suffers from communication and serial matching bottlenecks, creating an exponential decoding backlog that limits quantum execution. This paper presents a design automation and hardware-software co-design framework for real-time surface code decoding using symmetry-aware, low-bit quantized graph neural networks. Operating as a confidence-gated hardware pre-filter, the four-bit integer (INT4) decoder commits 73.4% to 94.0% of syndrome frames directly on silicon within deterministic sub-microsecond deadlines, routing only ambiguous degenerate frames to classical matching while preserving full logical fidelity. To prevent arithmetic collapse in fixed-point datapaths without increasing word length, lattice dihedral equivariance is incorporated as an algebraic variance regularizer that suppresses activation outliers. Automated clique projection converts irregular detector hypergraphs into bounded-degree topologies, enabling an initiation interval of one cycle on systolic pipelines. Evaluated across physical AMD Kintex UltraScale+ FPGA hardware telemetry and sign-off post-route SkyWater 130 nm standard-cell ASIC synthesis (room-temperature extractions at 25°C and 1.8 V evaluated analytically against a 1.5 W 4K cryostat cooling lift), the architecture delivers 106.2 to 396.8 ns execution latency with +0.18 ns positive static timing slack at 312.5 MHz clock frequency and 3.80 to 66.25 nJ energy per operation. Multi-server queueing analysis confirms queue stability under continuous 1 MHz syndrome streams, bounding average queue wait time well within physical qubit coherence limits. Note: This work has been submitted to the IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) for possible publication.