Noise-Induced Landscape Distortion in QAOA for Constrained Binary Optimization: Empirical Characterization on IBM Quantum Hardware

Abstract

We introduce and empirically validate Landscape Span Compression (LSC), a device-agnostic metric for quantifying how hardware noise distorts the variational energy landscape of the Quantum Approximate Optimization Algorithm (QAOA). Intuitively, LSC measures how much noise flattens the energy landscape, approaching 1 as the landscape collapses toward a barren plateau. We report an experience study of applying QAOA with LSC-based noise characterization on IBM's ibm_fez for three constrained QUBO portfolio instances, distilling practical lessons for parameter transfer, calibration-model fidelity, and error mitigation. Running p=1 QAOA on ibm_fez (Heron r2, 156 qubits) with up to 57,344 shots per grid point across three constrained binary optimization instances encoded as QUBO problems, we find: (i) hardware noise uniformly compresses the landscape span by 24-30% without displacing the global minimum, supporting classical-to-hardware parameter transfer; (ii) feasibility fractions at the optimal parameters remain 1.5-1.7 times above random sampling despite noise-induced degradation; (iii) the IBM calibration-based noise model achieves Pearson r=0.959 structural agreement with hardware but explains only approximately 42% of approximation-ratio degradation, with crosstalk and coherent errors as the leading unexplained contributors; (iv) a consistent noise cost of approximately 0.03 approximation-ratio units is observed across all instances; and (v) Zero-Noise Extrapolation yields mixed energy improvements of +7%/+9%/-4% per instance with 3-5 times uncertainty inflation. We compare LSC against four existing metrics and argue it is the most robust discriminator of noise severity for constrained QAOA on near-term devices.