  Multiclass classification is of great interest for various applications, for
example, it is a common task in computer vision, where one needs to categorize
an image into three or more classes. Here we propose a quantum machine learning
approach based on quantum convolutional neural networks for solving the
multiclass classification problem. The corresponding learning procedure is
implemented via TensorFlowQuantum as a hybrid quantum-classical (variational)
model, where quantum output results are fed to the softmax activation function
with the subsequent minimization of the cross entropy loss via optimizing the
parameters of the quantum circuit. Our conceptional improvements here include a
new model for a quantum perceptron and an optimized structure of the quantum
circuit. We use the proposed approach to solve a 4-class classification problem
for the case of the MNIST dataset using eight qubits for data encoding and four
ancilla qubits; previous results have been obtained for 3-class classification
problems. Our results show that accuracies of our solution are similar to
classical convolutional neural networks with comparable numbers of trainable
parameters. We expect that our finding provide a new step towards the use of
quantum neural networks for solving relevant problems in the NISQ era and
beyond.
