Related papers: Branch-and-Bound Tensor Networks for Exact Ground-…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum…
Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J.…
Computing the exact optimal experimental design has been a longstanding challenge in various scientific fields. This problem, when formulated using a specific information function, becomes a mixed-integer nonlinear programming (MINLP)…
Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based…
Modern data sources are typically of large scale and multi-modal natures, and acquired on irregular domains, which poses serious challenges to traditional deep learning models. These issues are partially mitigated by either extending…
Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the…
This paper presents a geometric analysis of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Due to the highly complicated structure of the associated sensing…
Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In…
Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…
We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…
Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization…
Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…
We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an…
Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…