Quantum Machine Learning

# Classical computing modules
import numpy as np
import pandas as pd
import seaborn as sns
from sklearn.neighbors import KNeighborsClassifier
from sklearn.neural_network import MLPClassifier
# Dataset
from sklearn import datasets, preprocessing 
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
# Quantum computing modules
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit_aer import AerSimulator
from qiskit.visualization import plot_histogram
from qiskit.quantum_info import Statevector

Iris Data Set

# Load the dataset
iris = datasets.load_iris()
feature_labels = iris.feature_names
class_labels = iris.target_names

# Extract the data
X = iris.data
y = np.array([iris.target])
M = 4 # M is the number of features in the data set

# Print the features and classes
print("Features: ", feature_labels)
print("Classes: ", class_labels)

Features:  ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']
Classes:  ['setosa' 'versicolor' 'virginica']

df = pd.DataFrame(data = np.concatenate((X, y.T), axis = 1), columns = feature_labels[0:M] + ["Species"])
sns.pairplot(df, hue = 'Species')

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

min_max_scaler = preprocessing.MinMaxScaler(feature_range=(0, 1))
min_max_scaler.fit(X)
X_normalized = min_max_scaler.transform(X)

normalized_iris = pd.DataFrame(data = np.concatenate((X_normalized, y.T), axis = 1), columns = feature_labels[0:M] + ["Species"])
sns.pairplot(normalized_iris, hue = 'Species')

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

K-Nearest Neighbors (Classical)

The following is modified from this code repo.

# First test out kNN with the non-normalized data
N_train = 100 # Training dataset size

X_train, X_test, y_train, y_test = train_test_split(X, y[0], train_size=N_train) # Random splitting
knn = KNeighborsClassifier(n_neighbors = 4)
knn.fit(X_train, y_train)
y_pred = knn.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)*100
print(accuracy)

96.0

# Now with the normalized data
N_train = 100 # Training dataset size

X_train, X_test, y_train, y_test = train_test_split(X_normalized, y[0], train_size=N_train)

knn = KNeighborsClassifier(n_neighbors = 4)
knn.fit(X_train, y_train)
y_pred = knn.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)*100
print(accuracy)

94.0

for k in range(1,21):
    knn = KNeighborsClassifier(n_neighbors = k)
    knn.fit(X_train, y_train)
    y_pred = knn.predict(X_test)
    accuracy = accuracy_score(y_test, y_pred)*100
    print(k, accuracy)

1 96.0
2 94.0
3 94.0
4 94.0
5 96.0
6 98.0
7 98.0
8 98.0
9 96.0
10 98.0
11 98.0
12 98.0
13 98.0
14 96.0
15 94.0
16 94.0
17 96.0
18 96.0
19 96.0
20 98.0

K-Nearest Neighbors (Quantum)

# Select a sample test sample for classification
# We will run through the algorithm with only a single test
# point to start.
test_index = int(np.random.rand()*len(X_test)) 
phi_test = X_test[test_index]
print("The test point in classical notation:", phi_test)

# Create the encoded feature vector, it needs to be a single
# vector which is normalized. We are translating classical data to
# quantum form.
# Iterate through each feature
for i in range(M):
    # Take a given feature and create a normalized vector of length
    # two with the vector
    phi_i = [np.sqrt(phi_test[i]), np.sqrt(1- phi_test[i])]

    # Create the variable phi_i, which will be the features encoded into
    # quantum information. Information is added to the vector with each
    # feature using a tensor product.
    if i == 0:
        phi = phi_i
    else:
        phi = np.kron(phi_i, phi)

print("The test point in quantum notation is:", phi)

The test point in classical notation: [0.72222222 0.5        0.79661017 0.91666667]
The test point in quantum notation is: [0.51351019 0.3184655  0.51351019 0.3184655  0.25947216 0.1609178
 0.25947216 0.1609178  0.15482915 0.09602096 0.15482915 0.09602096
 0.0782338  0.04851854 0.0782338  0.04851854]

# This cell constructs a quantum state which will encode the training data

# N is based off of the number of training points, 
# remember that M is the number of features.
N = int(np.ceil(np.log2(N_train)))
print("N:", N, "2^N:", 2**N)
# We need 2^(M+N) qubits to encode the training data, initilize
# the vector to be all zeros and the correct size
psi = np.zeros(2**(M + N)) 

# For each training point
for i in range(N_train):
    # Encode |i>, which has a one at the index of the number
    # of training points
    # 2^N is guaranteed to be bigger than N_train
    i_vec = np.zeros(2**N)
    i_vec[i] = 1

    # Encode |x>, the feature vector, using the same process
    # we used above to create the test state.
    x = X_train[i]
    for j in range(M):
        x_temp = [np.sqrt(x[j]), np.sqrt(1- x[j])]
        if j == 0:
            x_vec = x_temp
        else:
            x_vec = np.kron(x_temp, x_vec)
    # The final state for this training point is found with the tensor
    # product of |x> and |i>
    psi_i = np.kron(x_vec, i_vec)
    # Add the contribution from the current training point to the 
    # state. The goal is to encode information about every single 
    # training point into psi
    psi += psi_i
# Normalize
psi /= np.sqrt(N_train)

N: 7 2^N: 128

# This algorithm is based off of four quantum registers
# that will be combined to form the qubits

# This register handles encoding the indices of the training data
index_reg = QuantumRegister(N, 'i')
# This register holds the quantum representation of the training data
# features
train_reg = QuantumRegister(M, 'train')
# This one holds the test feature vector
test_reg = QuantumRegister(M, 'test')
# This single qubit is used to measure the similarity between
# the test and training points
p = QuantumRegister(1, 'similarity')

# Add each of the registers to a quantum circuit

# Create the quantum circuit
qknn = QuantumCircuit()

# Add registers to the circuit
qknn.add_register(index_reg)
qknn.add_register(train_reg)
qknn.add_register(test_reg)
qknn.add_register(p)

# Draw the quantum circuit
qknn.draw('mpl') 

# IMPORTANT: 2^n bits of information can be encoded into n qubits
# A 𝑛-qubit state can be represented by a linear combination of the 2𝑛 vectors of 
# the standard computational basis. To accurately describe a quantum state over 𝑛 
# qubits, you thus need 2𝑛 coefficients (aka amplitudes) which are complex numbers 
# in general.

# So index and training registers can encode psi, which as length 2^(M+N)
# and the test register can encode phi, which has length 2^M

# Initialize the training register using the state from above
qknn.initialize(psi, index_reg[0:N] + train_reg[0:M])

# Initialize the test register using the state from above
qknn.initialize(phi, test_reg)

# Draw qknn
qknn.draw('mpl')

def swap_test(N):
    '''
    `N`: Number of qubits of the quantum registers.
    '''
    a = QuantumRegister(N, 'a')
    b = QuantumRegister(N, 'b')
    d = QuantumRegister(1, 'd')
    
    # Quantum Circuit
    qc_swap = QuantumCircuit(name = ' SWAP \nTest')
    qc_swap.add_register(a)
    qc_swap.add_register(b)
    qc_swap.add_register(d)
    
    qc_swap.h(d)
    for i in range(N):
        qc_swap.cswap(d, a[i], b[i])
            
    qc_swap.h(d)    
    
    return qc_swap

# Apply the Quantum SWAP Test module to the quantum circuit
qknn.append(swap_test(M), train_reg[0:M] + test_reg[0:M] + [p[0]])
# Draw qknn
qknn.draw('mpl')

# Create the classical register
meas_reg_len = N + 1
meas_reg = ClassicalRegister(meas_reg_len, 'meas')
qknn.add_register(meas_reg)

# Measure the qubits
qknn.measure(index_reg[0::] + p[0::], meas_reg)

# Draw qknn
qknn.draw('mpl', fold = -1)

from qiskit import transpile
simulator = AerSimulator()
t_qknn = transpile(qknn, simulator)
counts_knn = simulator.run(t_qknn).result().get_counts()

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/urllib3/__init__.py:35: NotOpenSSLWarning: urllib3 v2 only supports OpenSSL 1.1.1+, currently the 'ssl' module is compiled with 'LibreSSL 2.8.3'. See: https://github.com/urllib3/urllib3/issues/3020
  warnings.warn(

result_arr = np.zeros((N_train, 3))
for count in counts_knn:
    i_dec = int(count[1::], 2)
    phase = int(count[0], 2)
    if phase == 0:
        result_arr[i_dec, 0] += counts_knn[count]
    else:
        result_arr[i_dec, 1] += counts_knn[count]

for i in range(N_train):        
    prob_1 = result_arr[i][1]/(result_arr[i][0] + result_arr[i][1])
    result_arr[i][2] = 1 - 2*prob_1

# Find the indexes of minimum distance
import scipy
k = 10
k_min_dist_arr = result_arr[:, 2].argsort()[::-1][:k]

# Determine the class of the test sample
y_pred = scipy.stats.mode(y_train[k_min_dist_arr])[0]
y_exp = y_test[test_index]
print('Predicted class of the test sample is {}.'.format(y_pred))
print('Expected class of the test sample is {}.'.format(y_exp))

Predicted class of the test sample is 2.
Expected class of the test sample is 2.

Neural Networks (Classical)

# Load the dataset
iris = datasets.load_iris()
feature_labels = iris.feature_names
class_labels = iris.target_names

# Extract the data
X = iris.data
y = np.array([iris.target])
print(type(y))
M = 4 # M is the number of features in the data set

# Print the features and classes
print("Features: ", feature_labels)
print("Classes: ", class_labels)

<class 'numpy.ndarray'>
Features:  ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']
Classes:  ['setosa' 'versicolor' 'virginica']

min_max_scaler = preprocessing.MinMaxScaler(feature_range=(0, 1))
min_max_scaler.fit(X)
X_normalized = min_max_scaler.transform(X)

N_train = 100
X_train, X_test, y_train, y_test = train_test_split(X, y[0], 
                                                train_size=N_train)

# hidden_layer_sizes: tuple describing the number of neurons in each hidden 
# layer
# activation: the activation function; ‘identity’, ‘logistic’, ‘tanh’, ‘relu’
# solver: the optimizer; ‘lbfgs’, ‘sgd’, ‘adam’
# max_iter: the maximum number of training iterations the neural network will 
# take to train
# tol: if the change in loss between one iteration and the next is less than 
# the tolerance, stop training (early stopping)
# Typically the loss function is also a hyperparameter, but is set here 
# (scikit-learn is the most restrictive nn implementation)
nn = MLPClassifier(hidden_layer_sizes=(4, 3, 2), activation='relu', 
                   solver='adam', max_iter=5000, tol=0.000001)
nn.fit(X_train, y_train)
y_pred = nn.predict(X_test)

accuracy = accuracy_score(y_test, y_pred)*100
print(accuracy)

96.0

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(

import matplotlib.pyplot as plt
loss_curve = nn.loss_curve_
plt.plot(range(len(loss_curve)), loss_curve)

hidden_layers = [(100), (10,10,10,10), (4,3,2), (5)]
activation = ['identity', 'logistic', 'tanh', 'relu']
max_iter = [100, 500, 1000, 5000]


best_accuracy = 0
best_params = []

for hl in hidden_layers:
    for a in activation:
        for mi in max_iter:
            nn = MLPClassifier(hidden_layer_sizes=hl, 
                               activation=a, solver='adam', 
                               max_iter=mi, tol=0.000001)
            nn.fit(X_train, y_train)
            y_pred = nn.predict(X_test)

            accuracy = accuracy_score(y_test, y_pred)*100

            if accuracy > best_accuracy:
                best_accuracy = accuracy
                best_params = [hl, a, mi]

print("Best Accuracy:", best_accuracy)
print("Best Hyperparameters:", best_params)

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.
  warnings.warn(
/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(

Best Accuracy: 100.0
Best Hyperparameters: [100, 'tanh', 100]

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.
  warnings.warn(

nn = MLPClassifier(hidden_layer_sizes=best_params[0], 
                   activation=best_params[1], solver='adam', 
                   max_iter=best_params[2], tol=0.000001)

nn.fit(X_train, y_train)

y_pred = nn.predict(X_test)

accuracy = accuracy_score(y_test, y_pred)*100
print(accuracy)

100.0

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(

X_train, X_test, y_train, y_test = train_test_split(X, y[0], 
                                            train_size=N_train)

nn = MLPClassifier(hidden_layer_sizes=best_params[0], 
                   activation=best_params[1], solver='adam', 
                   max_iter=best_params[2], tol=0.000001)

nn.fit(X_train, y_train)

y_pred = nn.predict(X_test)

accuracy = accuracy_score(y_test, y_pred)*100
print(accuracy)

100.0

/Users/butlerju/Library/Python/3.9/lib/python/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
  warnings.warn(

Quantum Neural Network Classifier

The below code is modified from the Qiskit Machine Learning tutorial on the variational quantum classifier.

The Variational Quantum Classifier (VQC) is a variational algorithm like the variational quantum eigensolver (VQE). It is a hybrid algorithm that computes its value with a quantum circuit, using an ansatz contain optimizable parameters. The parameters are optimized over several iterations using a classical optimizer.

!pip install qiskit_algorithms
!pip install qiskit_machine_learning

Defaulting to user installation because normal site-packages is not writeable
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: /Library/Developer/CommandLineTools/usr/bin/python3 -m pip install --upgrade pip
Defaulting to user installation because normal site-packages is not writeable
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: /Library/Developer/CommandLineTools/usr/bin/python3 -m pip install --upgrade pip

from qiskit.circuit.library import ZZFeatureMap
from qiskit.circuit.library import RealAmplitudes
from qiskit_machine_learning.algorithms.classifiers import VQC
from qiskit_algorithms.utils import algorithm_globals
from qiskit_algorithms.optimizers import COBYLA

from matplotlib import pyplot as plt
from IPython.display import clear_output

import time

# Get the number of features in the training data
num_features = len(X_normalized[0])

# The feauture map will encode the features of the training data. We need 
# to specify the number of features in the training data and apply it to 
# the circuit once. Note the values x[0], x[1], x[2], and x[3]. These will 
# be filled with the feature's once the neural network is run.

# This acts as the input layer in a classical neural network. Taking in the 
# data and preparing it to be passed to the rest of the network. This feature 
# map will appear first in the algorithm.
feature_map = ZZFeatureMap(feature_dimension=num_features, reps=1)
feature_map.decompose().draw(output="mpl", fold=-1)

# The real amplitudes function will create a parameterized circuit that will
#  act like the hidden layers of our network. We specify the number of qubits 
# in the circuit to be the number of features in the training data. We will 
# start the circuit with one repetition, giving us 8 parameters (theta[0] - 
# theta[7]) to optimize when training the neural network.

# Phrased another way, in the language of variational quantum algorithms, this 
# funciton is the ansantz of our quantum algorithm and its values theta willl 
# be optimized.

# Note that the number of reps can in increased here to increase the number of 
# trainable parameters (similar to increasing the number of neurons in a 
# classical neural network). However, the number of reps in the feature map must 
# remain at 1.

ansatz = RealAmplitudes(num_qubits=num_features, reps=1)
ansatz.decompose().draw(output="mpl")

# Define the list which will hold the values of the loss function
# every iteration
loss_func_vals = []

# This function will run with every training iteration of the quantum neural
# network. The function must take the current weights of the model (the values
#  of theta in the real amplitudes function) and the current value of the loss 
# function. This particular function creates a training iteration vs. loss 
# graph to see the value of the loss function as the network trains but in 
# principle this function can do anything.

def callback_graph(weights, loss_func_current):
    clear_output(wait=True)
    loss_func_vals.append(loss_func_current)
    plt.xlabel("Training Iteration")
    plt.ylabel("Loss Function Value")
    plt.plot(range(len(loss_func_vals)), loss_func_vals)
    plt.show()

# Define the optimizer that will be used to find the optimized values of 
# theta.
# maxiter is the number of training iterations the network will have. 
# This can be increased or decreased.
optimizer = COBYLA(maxiter=100)

# VQC stands for “variational quantum classifier.” It takes a feature 
# map and an ansatz and constructs a quantum neural network 
# automatically. We also need to pass the optimizer and the callback 
# function (this last one is optional). The loss function by default is
#  the cross entropy function, which is pretty standard for 
# classifications.
vqc = VQC(
    feature_map=feature_map,
    ansatz=ansatz,
    optimizer=optimizer,
    callback=callback_graph,
)

# Split the data into a training and test set, making sure to use 
# the normalized data
X_train, X_test, y_train, y_test = train_test_split(X_normalized, 
                                        y[0], train_size=N_train)

# clear loss value history
loss_func_vals = []

# Train the variational quantum classifier while also timing the process. 
# Note that the time does go down if you remove the callback function from 
# the initialization. Creating many graphs does take some time.
start = time.time()
vqc.fit(X_train, y_train)
elapsed = time.time() - start

# Print the total time needed to train the network
print(f"Training time: {round(elapsed)} seconds")

Training time: 39 seconds

# Compute the accuracy with the training data and the test data (aka 
# data it knows and data it has never seen before). Print the scores 
# after.
train_score_q4 = vqc.score(X_train, y_train)
test_score_q4 = vqc.score(X_test, y_test)

print(f"Quantum VQC on the training dataset:", 
      np.round(train_score_q4*100))
print(f"Quantum VQC on the test dataset:",
      np.round(test_score_q4*100))

Quantum VQC on the training dataset: 71.0
Quantum VQC on the test dataset: 68.0