Parameter Optimization and Noise Resilience Analysis for QAOA on NISQ Devices: A Comprehensive Study from 3 to 40 Qubits

Quantum algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices require optimization strategies matched to circuit structure. We present two complementary approaches: VERMICULAR, achieving 93.0% success rates for Grover’s algorithm through strategic dynamical decoupling (DD) placement (vs. 18.3% baseline), and systematic QAOA parameter optimization achieving 94.5% approximation ratios for MaxCut (vs. 39.6% with theoretical parameters). Through >15,000 circuit executions across IQM Garnet, Rigetti Ankaa-3, and IonQ Forte-1 (total cost: €70), we demonstrate that circuit structure determines which strategy succeeds: DD helps algorithms with substantial idle time (Grover: 34% idle → 5× improvement) but degrades continuously-active circuits (QAOA: 2.4% idle → 50% degradation with DD). We systematically characterize algorithm noise resilience via critical noise thresholds (σc), finding Bell states achieve 4× higher σc than product states (0.200 vs 0.050, p < 0.001) and that σc predicts hardware performance (r = 0.94, p = 0.006). QAOA scaling studies (3-40 qubits) reveal exponential decay with 56% plateau beyond 20 qubits. Simulator-optimized parameters transfer effectively to hardware (85-98% efficiency), but hardware-to-hardware transfer requires architecture-specific tuning. We provide SigmaCSuite, an open-source validation framework, and complete experimental protocols. These findings establish that optimization strategy must match circuit structure: idle-time protection for search algorithms, parameter tuning for variational algorithms—achieving 2.5-5× improvements through targeted approaches.