# Demo 1：QAOA K4 MaxCut

> 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（热图+top cuts） —— 11×11 网格 + 爬山

**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：K4 = 4-node complete graph, 6 edges. We scan the (γ, β) landscape for
     p=1 QAOA, plot ⟨H_C⟩ as a contour/heatmap, overlay a classical hill-climb
     trajectory that pushes past the grid optimum, then histogram the dominant
     bitstrings at the final (γ*, β*). For K4 the optimal cut = 4 and QAOA p=1
     typically attains ≈ 0.92 approximation ratio (Farhi et al. 2014).

## 完整源码

```{literalinclude} 01_qaoa_maxcut_4node.py
:language: python
:linenos:
:caption: demos/ch14-optimization-numerics/01_qaoa_maxcut_4node.py
```

## 运行结果

![Demo 1：QAOA K4 MaxCut](01_qaoa_maxcut_4node.png)

## 运行方式

```bash
# 仓库根目录执行；输出 PNG 到 demos/ch14-optimization-numerics/01_qaoa_maxcut_4node.png，关键统计到 stdout
.venv/bin/python3 demos/ch14-optimization-numerics/01_qaoa_maxcut_4node.py
```

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