Related papers: On Stability of Tensor Networks and Canonical Form…

We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function…

The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework underlying many of the analytical results derived through MPS,…

Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to…

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak…

We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…

We describe two developments of tensor network influence functionals (in particular, influence functional matrix product states (IF-MPS)) for quantum impurity dynamics within the fermionic setting of the Anderson impurity model. The first…

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…

Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…

We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size…

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical…

In this paper we show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a…

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…

Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or…

This paper accompanies with our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a…

The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS),…

Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…

We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all…