期待値計算でVQE。量子機械学習予行演習。

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pip install --no-deps -U git+https://github.com/jcmgray/quimb.git@develop autoray blueqat

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from blueqat import Circuit
from blueqat.pauli import Z

hamiltonian = 1*Z[0]+1*Z[1]
Circuit(4).x[:].run(backend="quimb", hamiltonian=hamiltonian)

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#量子ビット数
n = 100

#回路の繰り返し回数
p = 1

#必要なパラメータ数、(NN回路n*6)*繰り返し回数
n_params = (n * 6)*p

print("number of parameters=", n_params)

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#NN回路
def nn(params, n_qubits):
    c = Circuit()
    #1量子ビット任意回転
    for i in range(n_qubits):
        c.rx(params[i*3])[i].ry(params[i*3+1])[i].rz(params[i*3+2])[i]
    #2量子ビットクラスタ用CZ
    for i in range(n_qubits):
        c.cz[i, (i+1) % n_qubits]
    return c

#後処理
def post_process(params, n_qubits):
    c = Circuit()
    #1量子ビット任意回転
    for i in range(n_qubits):
        c.rx(params[i*3])[i].ry(params[i*3+1])[i].rz(params[i*3+2])[i]
    return c

#1サイクル分
def one_cycle(params, n_qubits):
    return nn(params[:3*n_qubits], n_qubits) + post_process(params[3*n_qubits:], n_qubits)

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def all_cycle(params, n_qubits, n_cycle):
    circuit = Circuit()
    
    for i in range(n_cycle):
        circuit += one_cycle(params[i*6*n:(i+1)*6*n], n_qubits)
        
    hamiltonian = 1*Z[n_qubits-1]
    return circuit.run(backend="quimb", hamiltonian=hamiltonian)

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%%time
import copy
import numpy as np
from blueqat.pauli import Z
import matplotlib.pyplot as plt

#ランダムパラメータ初期化
param = np.random.rand(n_params)*2*np.pi

#loss格納用のarray
arr = []

#学習率
e = 0.5

#微分
h = 0.1

loop = 10

for k in range(loop):
    #損失関数の代わりにハミルトニアン期待値をそのまま使う
    loss = all_cycle(param, n , p)
    arr.append(loss)
    
    #勾配法を実装します。
    loss_arr = np.zeros(n_params)
    for i in range(n_params):
        param_tmp = copy.copy(param)
        param_tmp[i] += h
        loss_arr[i] = all_cycle(param_tmp, n , p)
        
    param -= (loss_arr - loss)*e
    print("epoch:", k)
    print("loss:",loss)

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plt.plot(arr)
plt.show()