Related papers: DMRG Approach to Optimizing Two-Dimensional Tensor…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other…
We describe in detail the application of the recent non-Abelian Density Matrix Renormalization Group (DMRG) algorithm to the two dimensional t-J model. This extension of the DMRG algorithm allows us to keep the equivalent of twice as many…
Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods…
The density matrix renormalization group (DMRG) has become an indispensable numerical tool to find exact eigenstates of finite-size quantum systems with strong correlation. In the fields of condensed matter, nuclear structure and molecular…
Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…
Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states…
Sampling a quantum systems underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently…
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor…
Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful…