Matrix Product State

Matrix Product States (MPS) are tensor networks used to represent high-dimensional quantum states and increasingly, as efficient and interpretable models in machine learning. Current research focuses on developing novel MPS architectures, such as constrained MPS for optimization problems and those integrated with neural networks for enhanced performance in tasks like quantum simulation and time series generation. This work highlights MPS's ability to balance model expressiveness with computational tractability, leading to applications in diverse fields including quantum physics, cybersecurity, and finance, where interpretability and efficient training are crucial. The development of efficient training algorithms and the analysis of MPS generalization properties are also active areas of investigation.