相关论文: Locally accurate tensor networks for thermal state…

We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…

Preparing quantum thermal states on a quantum computer is in general a difficult task. We provide a procedure to prepare a thermal state on a quantum computer with a logarithmic depth circuit of local quantum channels assuming that the…

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…

The previously discussed anomalous behavior (i.e. negative) of the thermal expansion coefficient obtained from the pair correlation function is examined in the context of the nearest-neighbor distance (bond length) distribution. The bond…

In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations…

Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J.…

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…

This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…

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…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

We introduce a simple yet significant improvement to the time-evolving block decimation (TEBD) tensor network algorithm for simulating the time dynamics of strongly correlated one-dimensional (1D) mixed quantum states. The efficiency of 1D…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

An algorithm for imaginary time evolution of a fermionic projected entangled pair state (PEPS) with ancillas from infinite temperature down to a finite temperature state is presented. As a benchmark application, it is applied to spinless…

An accurate calculation of the properties of quantum many-body systems is one of the most important yet intricate challenges of modern physics and computer science. In recent years, the tensor network ansatz has established itself as one of…

Tensor network states have enjoyed great success at capturing aspects of strong correlation physics. However, obtaining dynamical correlators at non-zero temperatures is generically hard even using these methods. Here, we introduce a…

The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective…

We present an improved version of the algorithm contracting and optimizing finite projected entangled pair states (fPEPS) in conjunction with projected entangled pair operators (PEPOs). Our work has two components to it. First, we explain…

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…

We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the…