回答編集履歴
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test
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wikipedia先生によると対称になるのは[1,i]/sqrt(2)の時ですが…
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それが正しければ、ノルムの計算方法もまずいです。
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---
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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n = 100
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H = np.array([[1, 1],[1, -1]]) / np.sqrt(2)
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P = np.zeros((2, 2)); P[0, :] = H[0, :]
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Q = np.zeros((2, 2)); Q[1, :] = H[1, :]
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pos = np.zeros((2*n+1, 2), dtype=np.complex)
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pos[n, :] = np.array([1, 1j], dtype=np.complex) / np.sqrt(2)
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x = np.arange(-n, n+1)
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history = np.zeros((n, 2*n+1, 2), dtype=np.complex)
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history[0, :, :] = pos[:, :]
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prob = np.zeros((n, 2*n+1))
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prob[0, :] = np.sum(np.conj(history[0, :, :]) * history[0, :, :], axis=-1)[:]
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for t in range(1, n):
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history[t, :-1, :] += np.inner(history[t-1, 1:, :], P.T)
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history[t, 1:, :] += np.inner(history[t-1, :-1, :], Q.T)
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prob[t, :] = np.sum(np.conj(history[t, :, :]) * history[t, :, :], axis=-1)[:]
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history_ = np.zeros((n, 2*n+1))
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history_[0, n] = 1.
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for t in range(1, n):
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history_[t, :-1] += history_[t-1, 1:]/2.
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history_[t, 1:] += history_[t-1, :-1]/2.
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def show(x, y, y_=None, nonzeros=True):
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if nonzeros:
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s = 1
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ss = 2
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else:
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s = 0
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ss = 1
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plt.xlabel("x")
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plt.ylabel("probability")
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plt.ylim((0, np.max(y)*1.1))
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plt.xlim((np.min(x), np.max(x)))
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plt.plot(x[s::ss], y[s::ss], color="red", linewidth=1.0)
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if y_ is not None:
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plt.plot(x[s::ss], y_[s::ss], color="blue", linewidth=1.0)
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plt.grid()
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plt.savefig('q.png')
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plt.show()
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show(x, prob[-1], y_=history_[-1])
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```
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参考：
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https://arxiv.org/pdf/quant-ph/0303081.pdf
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Google画像: Quantum Random Walk
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edit
test
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@@ -5,3 +5,13 @@
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端の場所がおかしいのも問題ですね…
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---
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15
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wikipedia先生によると対称になるのは[1,i]/sqrt(2)の時ですが…
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17
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それが正しければ、ノルムの計算方法もまずいです。
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1
Edit
test
CHANGED
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@@ -1,3 +1,7 @@
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1
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s_listの更新のタイミングが悪いことと、
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確保してあるs_listのサイズが足りないことが問題だと思います。
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端の場所がおかしいのも問題ですね…
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