Recorded 07 February 2024. Feng Pan of the National University of Singapore presents "Arbitrary Tensor Network Algorithm: Theory, Methods and Applications" at IPAM's Tensor Networks Workshop. Abstract: In this talk, I will discuss about our trial in applying tensor network algorithms into modeling complex systems: arbitrary tensor network algorithm. This algorithm is designed to deal with the tensor network models corresponding to systems with arbitrary connections and give optionally approximate or exact results. The arbitrary tensor network algorithm will be introduced through three aspects: theory, methods and applications. For the theory part, the complexity lower bond of contracting an arbitrary tensor network and its connection to graph theory will be explained. The main focus of the method part will be how to construct both approximate and exact arbitrary tensor network algorithms. The core of constructing approximate arbitrary tensor network algorithms will be how to automatically and efficiently detect low-rank structures in tensor networks and how to control errors due to the low-rank approximations. While for constructing exact arbitrary tensor network algorithms, the key will be how to find appropriate contraction order and how to efficiently deploy contraction tasks into specific computing devices. Lastly, applications of arbitrary tensor network algorithms will be demonstrated, in both physical properties calculation in probabilistic graphical models and simulation of quantum circuits, especially using exact arbitrary tensor network algorithms to simulate random quantum circuit sampling experiments which were used to demonstrate "quantum supremacy". The progress made by arbitrary tensor network algorithms in this field is outstanding since the classical simulation time of the quantum experiments has been shortened to few dozens of seconds from the original 10,000 years, which fully demonstrates the power and potential of arbitrary tensor network algorithms. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/tensor-networks/