# Cerrado carbon-credit portfolio — QPC comparison task

## What this is

A **real-world replication** of the IBM quantum workflow in Ribeiro (2026), [arXiv:2602.09047](https://arxiv.org/abs/2602.09047), using the open dataset from [qaoa-carbon-cerrado](https://github.com/hgribeirogeo/qaoa-carbon-cerrado).

The goal is **not** to claim a new world-record portfolio score. The goal is to show that a **multi-objective business task** that vendors and papers typically treat as **one weighted QUBO + hybrid classical loop** (or **multiple separate quantum jobs**) can be expressed as **one polycontextural IBM submission**: three objective **contextures** on shared qubits, coupled by **transjunction** bridges, evaluated with the **same published portfolio metric**.

## Problem (same as Ribeiro 2026)

| Parameter | Value |
|-----------|--------|
| Region | Goiás municipalities, Brazilian Cerrado |
| Candidates | Top 128 by aggregate viability score → **n = 88** for quantum instance |
| Selection | Choose **k = 28** municipalities |
| Objectives | Carbon sequestration, biodiversity, social impact |
| Synergy weights | λ_C = 0.15, λ_B = 0.25, λ_S = 0.20 |
| Objective mix | w_c = 0.33, w_b = 0.33, w_s = 0.34 |

**Portfolio score** (identical to their `evaluate()`):

- Carbon: linear carbon scores + adjacency synergy  
- Biodiversity: linear scores + biome synergy + √(# distinct biomes) bonus  
- Social: linear scores + social synergy  
- Weighted sum → single scalar **portfolio score**

## Published baselines (their paper)

| Method | Portfolio score | Notes |
|--------|-----------------|-------|
| Greedy heuristic | **44.42** | Classical |
| QAOA + ZNE (7 runs, mean) | **~58.47** | `ibm_torino`, `ibm_fez`, p=1, warm-start |
| Simulated annealing | ~47 (varies) | 2 s budget |

Hardware: IBM Quantum, January 2026.

## Three workflows compared

### 1. Ribeiro baseline — single weighted QUBO + QAOA (+ ZNE on hardware)

One cost Hamiltonian combining all three objectives → one QAOA circuit → optional ZNE extrapolation. This is the **published quantum baseline**.

### 2. Sequential 3-job hybrid (Classiq-style)

Three **separate** quantum jobs:

1. Carbon-only QAOA  
2. Biodiversity-only QAOA  
3. Social-only QAOA  

Classical post-processing merges marginals (vote + greedy refinement) into one k=28 portfolio. **Same metric**, **three submissions**, typical industry pattern.

### 3. QPC polycontextural — one submission

One circuit on **n = 88 shared qubits**:

1. **Carbon contexture** — carbon linear + adjacency QUBO layer  
2. **Transjunction bridge** — ring CZ coupling  
3. **Biodiversity contexture** — biodiversity linear + biome synergy layer  
4. **Transjunction bridge**  
5. **Social contexture** — social linear + social synergy layer  
6. **Transjunction bridge**  
7. Shared XY-mixer (cardinality-preserving, warm-started from greedy)

One IBM job → sample → filter bitstrings with exactly 28 ones → **same `evaluate()` score**.

## Fair comparison rules

- **Same data** (`vendor_benchmarks/cerrado/data/`)  
- **Same n, k, λ, weights**  
- **Same portfolio score function**  
- **Same warm-start** (greedy solution) and QAOA angles (γ=0.05, β=0.20) where applicable  
- QPC run does **not** replicate ZNE unless explicitly added — compare architecture and score on equal footing; cite their ZNE mean as external reference

## How to run

```bash
cd site_release_2025_11_15

# Verify classical baseline matches paper (greedy ≈ 44.42)
python3 vendor_benchmarks/cerrado/qpc_cerrado_compare.py --mode verify

# Local Aer simulation (architecture comparison)
python3 vendor_benchmarks/cerrado/qpc_cerrado_compare.py --mode dry-run --shots 4096

# IBM Open hardware
export QISKIT_IBM_TOKEN=...
export QISKIT_IBM_INSTANCE=open-instance
python3 vendor_benchmarks/cerrado/qpc_cerrado_compare.py --mode ibm --backend ibm_fez --shots 4096
```

Results JSON: `results/cerrado_compare_*.json`  
Report page: `QPC_CERRADO_COMPARE.html`

## Files

| File | Role |
|------|------|
| `vendor_benchmarks/cerrado/cerrado_problem.py` | Data load, `evaluate()`, greedy, QUBO |
| `vendor_benchmarks/cerrado/cerrado_circuits.py` | Weighted QAOA + QPC 3-context circuit |
| `vendor_benchmarks/cerrado/qpc_cerrado_compare.py` | CLI runner |
| `docs/QPC_CERRADO_COMPARE_TASK.md` | This document |
| `QPC_CERRADO_COMPARE.html` | Public comparison report |

## Citation

Ribeiro, H. J. (2026). *QAOA with Zero Noise Extrapolation Outperforms Classical Heuristics for Carbon Credit Portfolio Optimization in Brazilian Cerrado.* arXiv:2602.09047.

QPC preprint: [10.5281/zenodo.20525931](https://doi.org/10.5281/zenodo.20525931)