Theoretical Studies on Classification and Representation of Physical States by Neural Networks

D. O. Oriekhov, Stan Bergkamp, Guliuxin Jin +5 more

Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here, we bridge the concept of a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses the real-space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone toward more accurate and better generalizable machine learning representations in condensed matter physics.

Ying Zhen Yang, Huaixin Cao, Zhanjun Zhang

Mihai n Bebe Simion, Dan Selișteanu, Dorin Șendrescu

Artificial Neural Networks are computing models that have been leading the progress in Machine Learning applications. In parallel, the first quantum computing devices have become available, paving the way for a new paradigm in information processing. Data representation is important for machine learning models. High-dimensional data can be converted to low dimensional codes efficiently by an artificial neural network. Due to quantum properties, a quantum algorithm can also perform this task, leaving only the neural network to perform the classification. In this paper, a quantum angle encoding algorithm is used to encode the vibration data into a binary representation, leaving the artificial neural networks for the classification. The vibration data in converted by applying a rotation on each of the Bloch sphere axes (X, Y and Z). After the rotation is performed, a measurement is made, collapsing the state into a single binary representation (0 or 1). Using the original and the converted data, multiple artificial neural networks topologies were trained to classify the data.

Huikang Huang, Haozhen Situ

Liam B. Schramm

Shengyao Wu, Runze Li, Yan-Qi Song +3 more

Neural network is a powerful learning paradigm for data feature learning in the era of big data. However, most neural network models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to address this problem. FDNN is a hierarchical deep neural network that derives information from both fuzzy and neural representations, the representations are then fused to form representation to be classified. FDNN perform well on uncertain data classification tasks. In this paper, we proposed a novel hierarchical fused quantum fuzzy neural network (HQFNN). Different from classical FDNN, HQFNN uses quantum neural networks to learn fuzzy membership functions in fuzzy neural network. We conducted simulated experiment on two types of datasets (Dirty-MNIST and 15-Scene), the results show that the proposed model can outperform several existing methods. In addition, we demonstrate the robustness of the proposed quantum circuit.