Demo 1：参数化 RY 扫描

第 2 章 量子神经网络 · 本章演示 · 代码演示总索引

可视化：单图曲线+误差条 —— 扫描 θ 画 ⟨Z⟩ = cos θ 曲线 + 误差标注

对应教程：第 2 章 量子神经网络 中相关小节 · 依赖安装：pip install "unified-quantum[visualization,simulation]"

实现要点

核心：演示参数化门 RY(θ)|0⟩ 的输出态在 Z 基下的期望值 ⟨Z⟩ = ⟨0|RY(θ)† Z RY(θ)|0⟩ = cos(θ) 扫描 θ ∈ [0, 2π]，对比理论 cos(θ) 曲线和量子线路测量值。

完整源码

demos/ch02-qnn/01_parametrized_rx_ry.py

"""
ch02-qnn demo 1: parameterised RY rotation scan

对应教程：chenzhaoyun.com/quantum-tutorial/ch02-quantum-nn/parametrized-gates-appendix.html
核心：演示参数化门 RY(θ)|0⟩ 的输出态在 Z 基下的期望值
       ⟨Z⟩ = ⟨0|RY(θ)† Z RY(θ)|0⟩ = cos(θ)
扫描 θ ∈ [0, 2π]，对比理论 cos(θ) 曲线和量子线路测量值。

依赖：pip install unified-quantum[visualization]
运行：python demos/ch02-qnn/01_parametrized_rx_ry.py
"""
from __future__ import annotations

from pathlib import Path

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np

from uniqc import Circuit, submit_task, wait_for_result

OUT = Path(__file__).parent

# === 1. 扫描参数，构建多条 1-qubit 线路 ===
N_POINTS = 24
thetas = np.linspace(0.0, 2 * np.pi, N_POINTS, endpoint=False)
shots = 4000

measured = np.zeros(N_POINTS)
for i, theta in enumerate(thetas):
    c = Circuit()
    c.ry(0, float(theta))
    c.measure(0)
    task_id = submit_task(circuit=c, backend="dummy:local:simulator", shots=shots)
    result = wait_for_result(task_id)
    probs = result.probabilities
    # ⟨Z⟩ = P(0) - P(1)
    measured[i] = probs.get("0", 0.0) - probs.get("1", 0.0)

theory = np.cos(thetas)

# === 2. matplotlib 可视化：理论 vs 测量，对照 cos(θ) 曲线 ===
fig, ax = plt.subplots(figsize=(8.5, 4.8))
ax.plot(thetas, theory, color="#1f77b4", lw=2.2, label=r"theory $\langle Z\rangle = \cos\theta$")
ax.plot(thetas, measured, "o", color="#d62728", ms=7, label=f"measured (shots={shots})")
ax.axhline(0.0, color="#888888", lw=0.7, ls="--")
ax.set_xlabel(r"rotation angle $\theta$ (rad)")
ax.set_ylabel(r"$\langle Z \rangle$")
ax.set_title("ch02-qnn demo 1: parameterised RY rotation — single-qubit expectation scan")
ax.set_xticks(np.linspace(0, 2 * np.pi, 5))
ax.set_xticklabels([r"$0$", r"$\pi/2$", r"$\pi$", r"$3\pi/2$", r"$2\pi$"])
ax.set_ylim(-1.15, 1.15)
ax.grid(alpha=0.3)
ax.legend(loc="upper right")

max_abs_err = float(np.max(np.abs(measured - theory)))
ax.text(
    0.02, 0.05,
    f"max |measured - cos θ| = {max_abs_err:.3f}",
    transform=ax.transAxes, fontsize=10,
    bbox=dict(boxstyle="round,pad=0.3", fc="#fff8dc", ec="#d4a017"),
)

plt.tight_layout()
out_path = OUT / "01_parametrized_rx_ry.png"
plt.savefig(out_path, dpi=120, bbox_inches="tight")
plt.close()

# === 3. stdout 关键统计 ===
print("ch02-qnn-demo-1: parameterised RY rotation scan")
print(f"  theta samples: {N_POINTS} over [0, 2π]")
print(f"  shots per sample: {shots}")
print(f"  max |measured - cos θ| = {max_abs_err:.4f}")
print(f"  measurement at θ=π   : ⟨Z⟩_meas = {measured[N_POINTS // 2]:+.4f} (theory = -1)")
print(f"  measurement at θ=π/2 : ⟨Z⟩_meas = {measured[N_POINTS // 4]:+.4f} (theory = 0)")
print(f"  PNG -> {out_path}")

运行结果

运行方式

# 仓库根目录执行；输出 PNG 到 demos/ch02-qnn/01_parametrized_rx_ry.png，关键统计到 stdout
.venv/bin/python3 demos/ch02-qnn/01_parametrized_rx_ry.py

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