Linear Structure of Training Samples in Quantum Neural Network Applications

Quantum Neural Networks (QNNs) use sets of training samples supplied as quantum states to approximate unitary operators. Recent results show that the average quality, measured as the error of the approximation, depends on the number of available training samples and the degree of entanglement of these samples. Furthermore, the linear structure of the training samples plays a vital role in determining the average quality of the trained QNNs. However, these results evaluate the quality of QNNs independently of the classical pre- and post-processing steps that are required in real-world applications. How the linear structure of the training samples affects the quality of QNNs when the classical steps are considered is not fully understood. Therefore, in this work, we experimentally evaluate QNNs that approximate an operator that predicts the outputs of a function from the automotive engineering area. We find that the linear structure of the training samples also influences the quality of QNNs in this real-world use case.