Related papers: Entangling Machine Learning with Quantum Tensor Ne…
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…
The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large, the corresponding weight matrices can be enormous,…
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 introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
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 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…
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…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…
Deep neural networks currently demonstrate state-of-the-art performance in several domains. At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required…
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…
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 investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…
Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated…