tensornetwerkmethoden

Tensor network methods are a class of algorithms used in physics and machine learning to represent and manipulate high-dimensional data. These methods leverage the mathematical structure of tensors, which are multi-dimensional arrays, to efficiently capture correlations and entanglement in complex systems. At their core, tensor networks decompose large, intractable tensors into a network of smaller, interconnected tensors. This decomposition allows for significant computational savings by reducing the storage and processing requirements compared to directly working with the original high-dimensional tensor.

Different types of tensor networks exist, each suited for specific problems. Common examples include Matrix Product States (MPS) for one-dimensional systems, Projected Entangled-Pair States (PEPS) for two-dimensional systems, and Tree Tensor Networks (TTN). The choice of tensor network architecture depends on the dimensionality and entanglement structure of the data being studied.

These methods find applications in various fields. In condensed matter physics, they are crucial for simulating quantum many-body systems, enabling the study of phenomena like superconductivity and magnetism. In machine learning, tensor networks are being explored for tasks such as dimensionality reduction, generative modeling, and representing complex probability distributions. Their ability to handle high-dimensional data efficiently makes them a powerful tool for tackling complex computational challenges.