Related papers: TTNOpt: Tree tensor network package for high-rank …
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…
Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
Quantization of weights of deep neural networks (DNN) has proven to be an effective solution for the purpose of implementing DNNs on edge devices such as mobiles, ASICs and FPGAs, because they have no sufficient resources to support…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary…
Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this…
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…
Characterizing the ground-state properties of disordered systems, such as spin glasses and combinatorial optimization problems, is fundamental to science and engineering. However, computing exact ground states and counting their…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
We present a systematic study of Tensor Network (TN) models $\unicode{x2013}$ Matrix Product States (MPS) and Tree Tensor Networks (TTN) $\unicode{x2013}$ for real-time jet tagging in high-energy physics, with a focus on low-latency…