Landscape Compression in Constrained QAOA Tracks Feasibility Loss on IBM Heron Hardware

Abstract:We study how hardware noise changes the p=1 Quantum Approximate Optimization Algorithm (QAOA) landscape for cardinality-constrained portfolio problems on ibm_fez (IBM Heron r2): seven instances from n=6 to 16 qubits, each on a 7x7 parameter grid at 4,096 and 8,192 shots per point. The first version of this paper proposed Landscape Span Compression (LSC), the fractional loss of energy range across the grid, as a device benchmark, based on stable values of 0.24-0.30 at n<=8. The larger study shows why that does not hold. Hardware LSC rises to 0.72-0.81 at n=16, growing with circuit size (R^2=0.96 and 0.88 for an exponential decay in CZ count). Because the landscape energy averages over all shots, it is nearly linear in the feasible fraction, and a statistic built only from that fraction reproduces LSC (Pearson r=0.954). For these penalty-encoded problems, landscape compression is a circuit-fidelity effect expressed as loss of feasible samples, as noise-flattening models of QAOA predict. The same mechanism biases the usual test of parameter transfer: grid verdicts on whether the optimum moves agree across shot counts for only 2 of 7 instances, and hardware optima move toward higher feasibility. Even in noiseless simulation, p=1 QAOA samples the feasible set of these instances almost uniformly, so best-feasible approximation ratios (>=0.9993) are uninformative and the only effect noise can remove is a raised feasible fraction. We withdraw the benchmark and noise-model-gap claims of the first version, correct its solution-quality figures, and describe a protocol that separates feasibility loss from solution quality.

7 pages, 4 figures, 7 tables. v2: substantially revised after a scaling study to n=16; withdraws the device-benchmark claim of v1 (changes listed in Sec. V). Data: doi:https://doi.org/10.5281/zenodo.23040298. Code: this https URL

Quantum Physics (quant-ph); Emerging Technologies (cs.ET)

arXiv:2604.19426 [quant-ph]

(or arXiv:2604.19426v2 [quant-ph] for this version)