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

Hugo José Ribeiro

TL;DR

This work demonstrates empirical quantum utility for environmental decision-making by applying Quantum Approximate Optimization Algorithm (QAOA) with Zero Noise Extrapolation (ZNE) to a real-world carbon credit portfolio problem in the Brazilian Cerrado. A fixed-depth, single-layer QAOA with an XY-mixer was run on 88 municipalities (k=28) using seven hardware executions across IBM Quantum backends, and ZNE extrapolation produced noise-free expectation values that consistently exceeded a classical greedy baseline (mean score 58.47 vs 44.42; p=0.0009; Cohen’s d=2.01). The approach integrated multi-objective criteria—carbon sequestration, biodiversity connectivity, and social impact—via a QUBO formulation with penalty-based cardinality constraints, using empirically calibrated coefficients and sparsification to fit NISQ hardware. Temporal stability was verified over a 13–17 day window with two backends, and bootstrap analyses supported the robustness of the reported improvements, establishing practical quantum utility for environmental optimization in a realistic setting. The study also provides a reproducible workflow, data sources, and code, outlining a scalable template for quantum-assisted territorial planning under current hardware constraints, while acknowledging limitations in claiming formal quantum advantage or solver-grade optimality.

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.

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

TL;DR

This work demonstrates empirical quantum utility for environmental decision-making by applying Quantum Approximate Optimization Algorithm (QAOA) with Zero Noise Extrapolation (ZNE) to a real-world carbon credit portfolio problem in the Brazilian Cerrado. A fixed-depth, single-layer QAOA with an XY-mixer was run on 88 municipalities (k=28) using seven hardware executions across IBM Quantum backends, and ZNE extrapolation produced noise-free expectation values that consistently exceeded a classical greedy baseline (mean score 58.47 vs 44.42; p=0.0009; Cohen’s d=2.01). The approach integrated multi-objective criteria—carbon sequestration, biodiversity connectivity, and social impact—via a QUBO formulation with penalty-based cardinality constraints, using empirically calibrated coefficients and sparsification to fit NISQ hardware. Temporal stability was verified over a 13–17 day window with two backends, and bootstrap analyses supported the robustness of the reported improvements, establishing practical quantum utility for environmental optimization in a realistic setting. The study also provides a reproducible workflow, data sources, and code, outlining a scalable template for quantum-assisted territorial planning under current hardware constraints, while acknowledging limitations in claiming formal quantum advantage or solver-grade optimality.

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.
Paper Structure (59 sections, 28 equations, 3 figures, 6 tables)

This paper contains 59 sections, 28 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Problem Formulation
  5. Carbon Credit Portfolio Optimization
  6. Dataset Construction and Variable Selection
  7. Carbon sequestration.
  8. Biodiversity.
  9. Social impact.
  10. Problem Formulation
  11. Decision variables.
  12. Multi-criteria objective function.
  13. Carbon term with spatial adjacency.
  14. Biodiversity term with biome synergy.
  15. Social term.
  16. ...and 44 more sections

Figures (3)

  • Figure 1: Overview of the carbon credit portfolio optimization workflow. (A) Construction of a QUBO matrix encoding linear and spatial quadratic contributions from carbon, biodiversity, and social criteria for $n = 88$ candidate municipalities. (B) Execution of QAOA circuits at increasing noise scale factors ($\lambda = 1, 2, 3$) on IBM Quantum hardware, followed by Zero Noise Extrapolation to estimate the noise-free expectation value. (C) Optimized portfolio for the Goiás Cerrado, highlighting the 28 selected municipalities out of 88 candidates.
  • Figure 2: Zero Noise Extrapolation (ZNE) diagnostics for carbon credit portfolio optimization ($n = 7$). Mean portfolio scores at noise scale factors $\lambda = 1, 2, 3$ with error bars (SD across runs). Linear (solid) and quadratic (dotted) fits extrapolate to the zero-noise limit ($\lambda = 0$). Shaded regions show 95% confidence intervals (bootstrap, $B = 100$). Dashed line: Greedy baseline (44.42). Individual scores at $\lambda > 1$ are diagnostic quantities not separately reported.
  • Figure 3: Consistency metrics across independent hardware executions of QAOA+ZNE. The analysis includes seven runs and a total of 172,032 measurement shots. (a) Success rates relative to the Greedy baseline, showing the fraction of runs satisfying each performance criterion. (b) Distribution of valid solution rates, defined as the percentage of shots satisfying the cardinality constraint, with the global mean indicated. (c) Jaccard similarity index between the quantum-selected portfolio and the Greedy selection, shown per run and grouped by hardware backend. The mean overlap is computed over runs with available bitstring telemetry ($n=6$).