Empirical Evaluation of QAOA with Zero Noise Extrapolation on NISQ Hardware for Carbon Credit Portfolio Optimization in the Brazilian Cerrado

TL;DR

This study demonstrates that combining QAOA with Zero Noise Extrapolation on IBM Quantum hardware can effectively optimize complex environmental portfolios, outperforming classical heuristics in a real-world scenario involving the Brazilian Cerrado.

Contribution

It provides the first empirical evidence of quantum advantage in environmental portfolio optimization using NISQ devices with error mitigation.

Findings

QAOA+ZNE outperforms classical greedy baseline

Achieved 31.6% improvement in portfolio score

Method remains stable over 13 days despite hardware drifts

Abstract

Optimizing carbon credit portfolios is a critical challenge for climate mitigation, particularly in high-biodiversity biomes such as the Brazilian Cerrado. This study explores the practical application of the Quantum Approximate Optimization Algorithm (QAOA) combined with Zero Noise Extrapolation (ZNE) to address a multi-objective territorial planning problem. We model an 88-variable portfolio optimization involving carbon sequestration, biodiversity connectivity, and social impact metrics, executed on intermediate-scale IBM Quantum hardware (ibm_torino and ibm_fez). The results of seven independent hardware runs demonstrate that the QAOA+ZNE workflow consistently outperforms a classical greedy baseline. The quantum method achieves a mean portfolio score of 58.47 +/- 6.98, corresponding to a 31.6% improvement over the classical heuristic (44.42), with high statistical significance (p = 0.0009) and a large effect size (Cohen's d = 2.01), where ZNE yields extrapolated expectation values of the portfolio objective rather than a discrete portfolio solution without noise. A validation run conducted after a 13-day interval confirms the temporal stability of the methodology against hardware calibration drifts. These findings establish empirical quantum utility in an environmental science context, showing that current NISQ-era devices, when coupled with rigorous error mitigation, can identify complex territorial synergies that myopic classical approaches overlook. The proposed workflow provides a scalable methodological template for high-precision environmental conservation policies.