# Demo 2：凸优化

> 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**：2 子图 —— FD 经典 vs Jordan 量子梯度

**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：2D convex quadratic f(x, y) = 0.5 (x-2)^2 + 0.5 (y+1)^2, gradient
     g(x, y) = (x-2, y+1). The convex-optimization chapter contrasts two
     oracle models:

       classical finite-difference gradient   = 2d function-value queries per step
       Jordan's quantum gradient (QPE + iQFT) = 1 coherent phase query per step

     Here d=2 → 4× query gap. Both loops run gradient descent with the
     same starting point and step size; the difference is the per-step
     query counter. The quantum loop builds the Jordan-style phase oracle
     explicitly so its OriginIR is visible — the analytical gradient is
     used for the actual descent step (the *full* Jordan oracle recovers
     it exactly given a sufficiently wide grid).

## 完整源码

```{literalinclude} 02_convex_optimization.py
:language: python
:linenos:
:caption: demos/ch14-optimization-numerics/02_convex_optimization.py
```

## 运行结果

![Demo 2：凸优化](02_convex_optimization.png)

## 运行方式

```bash
# 仓库根目录执行；输出 PNG 到 demos/ch14-optimization-numerics/02_convex_optimization.png，关键统计到 stdout
.venv/bin/python3 demos/ch14-optimization-numerics/02_convex_optimization.py
```

---

[← 本章演示](index.md) · [↑ 代码演示总索引](../index.md) · [⌂ 教程门户](https://tutorial.chenzhaoyun.com/)