Demo 2：|±⟩ 测量概率

第 1 章 量子计算基础 · 本章演示 · 代码演示总索引

可视化：4 根/基 柱状 —— 在 X/Y/Z 基上 P(0)/P(1) 分组柱图

对应教程：第 1 章 量子计算基础 中相关小节 · 依赖安装：pip install "unified-quantum[visualization,simulation]"

实现要点

为每个态跑 3 个电路（X/Y/Z 基测量），用柱状图对比 P(0)/P(1)。

完整源码

demos/ch01-basics/02_measurement_probability.py

"""
ch01-basics demo 2：|+> 与 |-> 在 X / Y / Z 三基上的测量概率

对应教程：chenzhaoyun.com/quantum-tutorial/chch01-basics/02-measurement-probability.html
依赖：pip install unified-quantum[visualization]
运行：python demos/ch01-basics/02_measurement_probability.py

为每个态跑 3 个电路（X/Y/Z 基测量），用柱状图对比 P(0)/P(1)。
"""

from uniqc import Circuit, submit_task, wait_for_result
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
from pathlib import Path

OUT = Path(__file__).parent

SHOTS = 2000


def measure(init_gates, basis):
    c = Circuit()
    for g in init_gates:
        if g == "h":
            c.h(0)
        elif g == "x":
            c.x(0)
    if basis == "X":
        c.h(0)
    elif basis == "Y":
        c.sdg(0)
        c.h(0)
    c.measure(0)
    tid = submit_task(circuit=c, backend="dummy:local:simulator", shots=SHOTS)
    r = wait_for_result(tid)
    total = sum(r.counts.values())
    p0 = r.counts.get("0", 0) / total
    return p0, 1.0 - p0


# === 1. Two input states ===
SCENARIOS = [
    ("|+> = H|0>",   ["h"]),
    ("|-> = H X|0>", ["x", "h"]),
]
BASES = ["Z", "X", "Y"]
LABEL0 = {"Z": "P(|0>)", "X": "P(|+>)", "Y": "P(|+i>)"}
LABEL1 = {"Z": "P(|1>)", "X": "P(|->)",  "Y": "P(|-i>)"}

rows = []
for state_name, init in SCENARIOS:
    for basis in BASES:
        p0, p1 = measure(init, basis)
        rows.append((state_name, basis, p0, p1))
        print(f"  {state_name:12s} basis={basis}: P(0)={p0:.3f}  P(1)={p1:.3f}")

# === 2. Grouped bar chart: x-axis = basis, grouped bars per input state ===
fig, ax = plt.subplots(figsize=(8.5, 5))
x = np.arange(len(BASES))
width = 0.18
colors = ["#1f77b4", "#ff7f0e", "#2ca02c", "#d62728"]

# Two states × two outcomes → 4 bars per basis group
for j, (state_name, _) in enumerate(SCENARIOS):
    for k, outcome in enumerate(["P(0)", "P(1)"]):
        heights = [
            next(r[2 + k] for r in rows
                 if r[0] == state_name and r[1] == basis)
            for basis in BASES
        ]
        offset = (j * 2 + k - 1.5) * width
        bars = ax.bar(x + offset, heights, width,
                      color=colors[j * 2 + k],
                      label=f"{state_name} {outcome}")
        for b, h in zip(bars, heights):
            ax.text(b.get_x() + b.get_width() / 2, h + 0.01, f"{h:.2f}",
                    ha="center", va="bottom", fontsize=7)

ax.set_xticks(x)
ax.set_xticklabels([f"{b} basis" for b in BASES], fontsize=11)
ax.set_ylabel("Probability", fontsize=11)
ax.set_ylim(0, 1.12)
ax.set_title("Measurement of |+> and |-> in Z / X / Y bases "
             f"(shots={SHOTS})", fontsize=12)
ax.legend(loc="upper right", fontsize=8, ncol=2)
ax.grid(axis="y", alpha=0.3)
plt.tight_layout()
plt.savefig(OUT / "02_measurement_probability.png", dpi=120, bbox_inches="tight")
plt.close()

# === 3. stdout 关键统计 ===
print("ch01-basics-demo-2: |+> and |-> in three Pauli bases")
print(f"  shots per circuit: {SHOTS}, total circuits: {len(rows)}")
print(f"  ideal: |+> → Z=(0.5,0.5) X=(1,0) Y=(0.5,0.5);  "
      f"|-> → Z=(0.5,0.5) X=(0,1) Y=(0.5,0.5)")

运行结果

运行方式

# 仓库根目录执行；输出 PNG 到 demos/ch01-basics/02_measurement_probability.png，关键统计到 stdout
.venv/bin/python3 demos/ch01-basics/02_measurement_probability.py

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