# Demo 3：QAOA 投资组合

> 第 14 章 优化与数值量子算法 · [本章演示](index.md) · [代码演示总索引](../index.md)

**可视化**：双图 —— 3 资产 Markowitz QUBO

**对应教程**：[第 14 章 优化与数值量子算法 中相关小节](https://tutorial.chenzhaoyun.com/quantum-tutorial/ch14-optimization-numerics/) · 依赖安装：`pip install "unified-quantum[visualization,simulation]"`

## 实现要点

核心：Toy Markowitz portfolio over 3 assets A, B, C with expected returns
     μ = (0.10, 0.15, 0.08), covariance Σ, risk aversion λ = 4.0, and a
     cardinality penalty that biases toward 2-asset portfolios. The
     quadratic utility is encoded as a QUBO H_C (negated because uniqc's
     qaoa_ansatz MAXIMIZES ⟨H_C⟩) and solved by p=1 QAOA. We sweep (γ, β),
     overlay a classical hill-climb trajectory, then histogram the top
     bitstrings at the optimum — the dominant sampling peaks correspond
     to the asset subsets QAOA suggests holding.

## 完整源码

```{literalinclude} 03_qaoa_portfolio.py
:language: python
:linenos:
:caption: demos/ch14-optimization-numerics/03_qaoa_portfolio.py
```

## 运行结果

![Demo 3：QAOA 投资组合](03_qaoa_portfolio.png)

## 运行方式

```bash
# 仓库根目录执行；输出 PNG 到 demos/ch14-optimization-numerics/03_qaoa_portfolio.png，关键统计到 stdout
.venv/bin/python3 demos/ch14-optimization-numerics/03_qaoa_portfolio.py
```

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