Related papers: Automatic structural optimization of tree tensor n…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

Twist fields are a powerful formal tool to compute R\'enyi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly…

The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…

It is widely recognized that the deeper networks or networks with more feature maps have better performance. Existing studies mainly focus on extending the network depth and increasing the feature maps of networks. At the same time,…

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…

We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network.…

With the advent of quantum and quantum-inspired machine learning, adapting the structure of learning models to match the structure of target datasets has been shown to be crucial for obtaining high performance. Probabilistic models based on…

In this paper, we review hyperparameter optimization methods for machine learning models, with a particular focus on the Adaptive Tree-Structured Parzen Estimator (ATPE) algorithm. We propose several modifications to ATPE and assess their…

Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…

Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in…

The electric power distribution network (PDN) and the transportation network (TN) are generally operated/coordinated by different entities. However, they are coupled with each other due to electric vehicle charging stations (EVCSs). This…

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…

Sparse neural networks are important for achieving better generalization and enhancing computation efficiency. This paper proposes a novel learning approach to obtain sparse fully connected layers in neural networks (NNs) automatically. We…

We introduce Quantum Tree Networks (QTN), an architecture for hierarchical multi-flow entanglement routing. The network design is a $k$-ary tree where end nodes are situated on the leaves and routers at the internal nodes, with each node…