Related papers: Tree tensor network hierarchical equations of moti…
We generalize time-evolving matrix product operators method to nonequilibrium quantum transport problems. The nonequilibrium current is obtained via numerical differentiation of the generating functional which is represented as a tensor…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the…
We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath…
In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…
We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
This study presents a novel state estimation approach integrating Deep Neural Networks (DNNs) into Moving Horizon Estimation (MHE). This is a shift from using traditional physics-based models within MHE towards data-driven techniques.…
We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…
We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two…
Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this…
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields.…
Computing spectral functions in large, non-periodic super-moir\'e systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing…
Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time…
A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to…
The machine learning approaches are applied in the dynamical simulation of open quantum systems. The long short-term memory recurrent neural network (LSTM-RNN) models are used to simulate the long-time quantum dynamics, which are built…
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…
Transformer-based methods have achieved state-of-the-art performance in time series forecasting (TSF) by capturing positional and semantic topological relationships among input tokens. However, it remains unclear whether existing…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…