回答編集履歴
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edit
test
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@@ -64,6 +64,10 @@
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---
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pythonでnumpyを使って書くと以下になります。
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（拡散行列は更新されてはいけないのですね。修正しました。）
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n = 2**
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n = 2**3
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itr = 8
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@@ -139,3 +143,181 @@
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print(np.argmax(psi*psi))
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```
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---
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sympyで自分で頑張る版。
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実際はHadamardGateを使って初期状態を準備しますが、シンボリックで割り算をしてしまって大変なことになるので、無理やり一度実数で割っています。
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IdentityGateなので使わなくてもいいのに、無駄に使って計算時間が少し増えています。
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```python
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import itertools
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from sympy.physics.quantum.qubit import Qubit, measure_all
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from sympy.physics.quantum.dagger import Dagger
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from sympy.physics.quantum.qapply import qapply
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from sympy.physics.quantum.gate import HadamardGate, IdentityGate
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from math import sqrt
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import matplotlib.pyplot as plt
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import functools
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import operator
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def prod(iterable):
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return functools.reduce(operator.mul, iterable, 1)
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n = 3
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itr = 8
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f_ = [0]*n
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f_[1] = 1
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fa = Qubit(*f_)
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basis = []
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for psi_ in itertools.product([0,1], repeat=n):
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basis.append(Qubit(*psi_))
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psi0 = sum(basis)/sqrt(2**n)
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psi = sum(basis)/sqrt(2**n)
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Hs = prod([HadamardGate(i) for i in range(n)])
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Is = prod([IdentityGate(i) for i in range(n)])
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'''
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p_ = [0]*n
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p = Qubit(*p_)
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psi0 = qapply(Hs*p).doit()
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psi = qapply(Hs*p)
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'''
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Uf = lambda q: qapply(Is*q - 2*fa*Dagger(fa)*q)
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Us = lambda q: qapply(2*psi0*Dagger(psi0)*q - Is*q)
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for i in range(itr):
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psi = Us(Uf(psi))
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y = [v[1] for v in measure_all(psi)]
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x = [''.join(map(str, v[0].qubit_values)) for v in measure_all(psi)]
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plt.plot(x, y, marker='.', label=i)
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print(y)
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plt.grid()
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plt.yscale('log')
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plt.legend()
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plt.show()
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```
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---
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grover見つけちゃったから答え合わせ版。
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操作回数によって逆に振幅が下がるのが気持ち悪いのですが、ライブラリの実装と同じ結果になるので、ビット数が少なくて、操作回数が少ないことが原因だと思い込むことにします。
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```python
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from sympy.physics.quantum.qapply import qapply
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from sympy.physics.quantum.qubit import IntQubit, Qubit, measure_all
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from sympy.physics.quantum.grover import OracleGate
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from sympy.physics.quantum.grover import superposition_basis
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from sympy.physics.quantum.grover import grover_iteration, apply_grover
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import matplotlib.pyplot as plt
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numqubits = 3
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f = lambda qubits: qubits == IntQubit(4)
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v = OracleGate(numqubits, f)
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q = superposition_basis(numqubits)
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for i in range(8):
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q = qapply(grover_iteration(q, v))
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ans = qapply(apply_grover(f, numqubits, iterations=i+1))
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y = [v[1] for v in measure_all(q)]
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x = [''.join(map(str, v[0].qubit_values)) for v in measure_all(q)]
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plt.plot(x, y, label=i)
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print(q)
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print(ans)
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plt.legend()
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plt.grid()
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plt.yscale('log')
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plt.show()
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```
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1
edit
test
CHANGED
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@@ -66,6 +66,8 @@
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66
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67
67
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pythonでnumpyを使って書くと以下になります。
|
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68
68
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69
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+
（拡散行列は更新されてはいけないのですね。修正しました。）
|
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70
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+
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69
71
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70
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```python
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@@ -80,13 +82,17 @@
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n =
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n = 2**4
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itr = 8
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f1 = np.zeros(n)
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r = np.random.randint(n)
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print(r)
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f1[r] = 1
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@@ -106,7 +112,7 @@
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def Us(v):
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new = 2*np.matmul(np.ones((n,n))/n, v) - np.matmul(np.eye(n), v)
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return new / np.linalg.norm(new)
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psi = Us(Uf(psi))
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plt.plot(psi*psi)
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plt.plot(psi*psi, label=i)
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plt.yscale('log')
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plt.grid()
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plt.legend()
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plt.show()
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