Demo 2：Bernstein-Vazirani

第 4 章 经典量子算法 · 本章演示 · 代码演示总索引

可视化：双子图（测量柱+oracle 示意） —— 4-qubit 一次查询读出隐藏 s=1011

对应教程：第 4 章 经典量子算法 中相关小节 · 依赖安装：pip install "unified-quantum[visualization,simulation]"

实现要点

经典查询需要 n=4 次, BV 算法只用 1 次即可读出 s. 构造 Oracle: f(x) = s . x (mod 2), 对 s 的每一位 s_i=1 的输入 qubit 施加 CNOT(i, output). 末态 H 后测量, 应 100% 命中 s.

完整源码

demos/ch04-classic-algorithms/02_bv_4qubit.py

"""
ch04 演示 2: Bernstein-Vazirani 算法, n=4, 隐藏字符串 s=1011.
经典查询需要 n=4 次, BV 算法只用 1 次即可读出 s.
构造 Oracle: f(x) = s . x (mod 2), 对 s 的每一位 s_i=1
的输入 qubit 施加 CNOT(i, output). 末态 H 后测量, 应 100% 命中 s.

对应教程: chenzhaoyun.com/quantum-tutorial/ch04-classic-algorithms/bernstein-vazirani-algorithm-tutorial.html
依赖: pip install unified-quantum[visualization]
运行: python demos/ch04-classic-algorithms/02_bv_4qubit.py
"""
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
N_INPUT = 4
N_OUTPUT = 1
N_QUBITS = N_INPUT + N_OUTPUT
S = (1, 0, 1, 1)  # hidden string, s_0 s_1 s_2 s_3
S_STR = "".join(str(b) for b in S)


def build_bv_circuit(secret_bits):
    """构造完整的 BV 电路: X on output, H on all, oracle (CNOT chains),
    H on input, 测量 input. secret_bits 是 (s_0, ..., s_{n-1}) 元组."""
    c = Circuit()
    c.x(N_INPUT)
    for q in range(N_QUBITS):
        c.h(q)
    for i, s_i in enumerate(secret_bits):
        if s_i == 1:
            c.cnot(i, N_INPUT)
    for q in range(N_INPUT):
        c.h(q)
    for q in range(N_INPUT):
        c.measure(q)
    return c


c_bv = build_bv_circuit(S)
tid = submit_task(circuit=c_bv, backend="dummy:local:simulator", shots=SHOTS)
result = wait_for_result(tid)
counts = result.counts

total = sum(counts.values())
labels = [f"{i:0{N_INPUT}b}" for i in range(2 ** N_INPUT)]

# bitstring 在 uniqc counts 中是反向的: bitstring[i] = qubit[n-1-i], 长度等于 n_qubits.
# 未被测量的 qubit (这里是 q[4], output) 在 bitstring 中默认为 0, 不影响输入解读.
def key_to_input_bits(bs):
    """把 counts 里的 bitstring 截取成 q[0..3] 的输入比特串."""
    return bs[-(N_INPUT):][::-1]


input_counts = {}
for bs, cnt in counts.items():
    inp = key_to_input_bits(bs)
    input_counts[inp] = input_counts.get(inp, 0) + cnt
vals = np.array([input_counts.get(lbl, 0) for lbl in labels])

correct_counts = 0
mismatches = []
for inp, cnt in input_counts.items():
    if inp == S_STR:
        correct_counts += cnt
    else:
        mismatches.append((inp, cnt))


fig, axes = plt.subplots(1, 2, figsize=(13, 4.8))

ax = axes[0]
colors = ["#d62728" if lbl == S_STR else "#1f77b4" for lbl in labels]
ax.bar(np.arange(len(labels)), vals / total * 100, color=colors, edgecolor="black")
ax.set_xticks(np.arange(len(labels)))
ax.set_xticklabels(labels, rotation=0, fontsize=8)
ax.set_xlabel("input register measurement  (q3 q2 q1 q0)")
ax.set_ylabel("probability (%)")
ax.set_title(
    f"BV measurement on input qubits\nred bar = s = {S_STR}, expect 100%"
)
for i, lbl in enumerate(labels):
    if vals[i] > 0:
        ax.text(i, vals[i] / total * 100 + 1.5,
                f"{vals[i]/total*100:.1f}%", ha="center", va="bottom", fontsize=7)
ax.set_ylim(0, 115)
ax.grid(axis="y", alpha=0.3)

ax = axes[1]
ax.barh(range(N_INPUT), [1 if b == 1 else 0 for b in S[::-1]],
        color="#1f77b4", edgecolor="black")
ax.set_yticks(range(N_INPUT))
ax.set_yticklabels([f"q[{i}]  (s_{i})" for i in range(N_INPUT - 1, -1, -1)])
ax.set_xticks([0, 1])
ax.set_xticklabels(["0", "1"])
ax.set_xlabel("oracle bit s_i (1 = CNOT(q[i], output) is applied)")
ax.set_title(f"Oracle structure for s = {S_STR}\nf(x) = x_0 XOR x_2 XOR x_3 (mod 2)")
ax.set_xlim(-0.05, 1.4)
for i, b in enumerate(S[::-1]):
    if b == 1:
        ax.text(1.05, i, "CNOT", va="center", fontsize=9, color="darkred")
ax.grid(axis="x", alpha=0.3)

fig.suptitle(
    f"Bernstein-Vazirani n={N_INPUT}, s={S_STR}  "
    f"(shots={SHOTS}, dummy:local:simulator)",
    fontsize=12, y=1.02,
)
plt.tight_layout()
plt.savefig(OUT / "02_bv_4qubit.png", dpi=120, bbox_inches="tight")
plt.close()


p_correct = correct_counts / total
print("ch04-classic-algorithms demo 2: Bernstein-Vazirani n=4, s=1011")
print(f"  shots: {total}")
print(f"  hidden string: s = {S_STR}")
print(f"  P(measured = s) = {p_correct:.4f}")
print(f"  unique measurement outcomes: {int((vals > 0).sum())}")
if mismatches:
    print(f"  mismatches (top 3): {mismatches[:3]}")
else:
    print("  no mismatches: every shot recovered s exactly")
print(f"  saved: {OUT / '02_bv_4qubit.png'}")

运行结果

运行方式

# 仓库根目录执行；输出 PNG 到 demos/ch04-classic-algorithms/02_bv_4qubit.png，关键统计到 stdout
.venv/bin/python3 demos/ch04-classic-algorithms/02_bv_4qubit.py

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