A Unified Framework for Calibration, Decoding, and Resource-Aware Processing in Hybrid Quantum-Classical Machine Learning

NISQ devices are bottlenecked by three coupled problems: drifting qubit frequencies, slow classical syndrome decoding (MWPM), and shot-noise in gradients. QCOP is the first closed-loop system that solves all three together inside a single GPU-accelerated pipeline: Spectral Calibration Engine (real-time drift correction) Hierarchical Syndrome Decoder (HSD) (volumetric, spatiotemporal surface-code decoder) Observable Compression Layer (end-to-end trainable shot-noise-aware compression) Key results (device-calibrated simulators, n=20 seeds): Up to 2× wall-clock VQE training speedup ≈40% reduction in VQE energy error vs. unaugmented baseline HSD beats MWPM by 2.5× latency and 2.9× logical error rate at distance d=13 Hardware pilot (ibm_nairobi, d=5, 2000 syndrome volumes): HSD delivers 1.6× latency reduction + 1.9× logical error rate reduction — directionally matches simulation but quantitatively smaller (expected extra noise sources). Three new theoretical bounds prove the joint gains on logical error rate, convergence rate, and observable variance. Full end-to-end hardware validation is ongoing (planned: ibm_kyoto/torino, Quantinuum H-series, larger distances). Why it matters: QCOP turns calibration, decoding, and observable post-processing from separate offline steps into a single, synergistic real-time control layer — a practical step toward making hybrid quantum-classical ML viable on today’s noisy hardware and scalable toward early fault-tolerant regimes. Figures & tables in the paper show: Decoding latency/LER scaling (Fig. 1, Table 1) Training speedup across VQE, kernel, molecular simulation (Fig. 2) Energy error vs. qubit count (Fig. 3) Loss convergence with theoretical bound (Fig. 4) Full ablation, sensitivity, and cross-hardware generalization tables Reproducible with one-command scripts on Qiskit Aer + pytket-qulacs using published device-calibrated noise models.