Tensor-networks for High-order Polynomial Approximation: A Many-body Physics Perspective

2022/04/16 by Tong Yang, Yang, Tong
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2204.07743

openalex publication_date 2022/04/16 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

Abstract

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a high-order nonlinear dynamics modeling problem, tensor-network models are investigated and exhibit promising modeling advantages. This novel perspective establish a connection between quantum information and functional approximation, which worth further exploration in future research.

Related

• Tensor Network States with Low-Rank Tensors
• Quantum computation and the evaluation of tensor networks
• Tensor Networks: a quantum-information perspective on numerical renormalization groups
• Quantum mechanics is *-algebras and tensor networks
• Entanglement-entropy-based scaling relation in QAOA tensor network simulations for the MAXCUT problem