  Image recognition is one of the primary applications of machine learning
algorithms. Nevertheless, machine learning models used in modern image
recognition systems consist of millions of parameters that usually require
significant computational time to be adjusted. Moreover, adjustment of model
hyperparameters leads to additional overhead. Because of this, new developments
in machine learning models and hyperparameter optimization techniques are
required. This paper presents a quantum-inspired hyperparameter optimization
technique and a hybrid quantum-classical machine learning model for supervised
learning. We benchmark our hyperparameter optimization method over standard
black-box objective functions and observe performance improvements in the form
of reduced expected run times and fitness in response to the growth in the size
of the search space. We test our approaches in a car image classification task
and demonstrate a full-scale implementation of the hybrid quantum ResNet model
with the tensor train hyperparameter optimization. Our tests show a qualitative
and quantitative advantage over the corresponding standard classical tabular
grid search approach used with a deep neural network ResNet34. A classification
accuracy of 0.97 was obtained by the hybrid model after 18 iterations, whereas
the classical model achieved an accuracy of 0.92 after 75 iterations.
