حالات الكيوبت والتراكب الكمي

import numpy as np

ket0 = np.array([1, 0], dtype=complex)
ket1 = np.array([0, 1], dtype=complex)
plus = (ket0 + ket1) / np.sqrt(2)
minus = (ket0 - ket1) / np.sqrt(2)

for name, state in [("|0>", ket0), ("|+>", plus), ("|->", minus)]:
    probs = np.abs(state) ** 2
    print(f"{name}: P(0) = {probs[0]:.3f}, P(1) = {probs[1]:.3f}")

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(42)
plus = np.array([1, 1]) / np.sqrt(2)
probs = np.abs(plus) ** 2

shots = 1000
outcomes = rng.choice([0, 1], size=shots, p=probs)
counts = [int(np.sum(outcomes == 0)), int(np.sum(outcomes == 1))]
print("النتائج:", {"0": counts[0], "1": counts[1]})

fig, ax = plt.subplots(figsize=(4.5, 3.2))
ax.bar(["|0>", "|1>"], counts, color=["#0D5C43", "#22C55E"])
ax.set_ylabel("count")
ax.set_title("1000 shots on |+>")
plt.show()

import numpy as np

plus = np.array([1, 1]) / np.sqrt(2)
global_phase = np.exp(1j * np.pi / 3) * plus
minus = np.array([1, -1]) / np.sqrt(2)

print("احتمالات |+>          :", np.round(np.abs(plus) ** 2, 4))
print("احتمالات e^{iθ}|+>    :", np.round(np.abs(global_phase) ** 2, 4))
print("تداخل مع |+> للحالة |->:", round(float(np.abs(np.vdot(plus, minus)) ** 2), 6))