Related papers: Time evolution of the quantum Ising model in two d…

Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…

We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state…

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

We study a variation of the Trotter-Suzuki decomposition, in which a Hamiltonian exponential is approximated by an ordered product of two-qubit operator exponentials such that the Trotter step size is enhanced for a small number of terms.…

Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

We study infinite limits of neural network quantum states ($\infty$-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of Renyi entropies are expressed in…

This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…

Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by…

We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. Whereas the usual approach starts from infinite temperature and evolves the state in imaginary time (toward…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…

A new numerical approach to entanglement entropies of the Renyi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited…

Quantum many-body systems out of equilibrium pose some of the most intriguing questions in physics. Unfortunately, numerically keeping track of time evolution of states under Hamiltonian dynamics constitutes a severe challenge for all known…

We determine the computational power of isometric tensor network states (isoTNS), a variational ansatz originally developed to numerically find and compute properties of gapped ground states and topological states in two dimensions. By…

Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…

Tensor networks are adopted to calculate the responses for one-dimensional quantum spin systems that are initially in thermal equilibrium. The Ising chain in mixed transverse and longitudinal fields is used as the benchmarking system. The…

A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…