Related papers: Quantum-Inspired Tensor Networks for Approximating…
Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks…
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 networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…
Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
In this paper, we introduce a new interpolation scheme to approximate the density of states (DOS) for a class of rank-structured matrices with application to the Tamm-Dancoff approximation (TDA) of the Bethe-Salpeter equation (BSE). The…
We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information…
Quantum Key Distribution (QKD) networks require routing methodologies capable of jointly optimizing latency, secret key generation rate, congestion, finite capacity and operational security constraints under dynamically evolving traffic…
Tensor Networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform Machine Learning (ML) tasks, yielding comparable results to standard…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
Quantum turbulence spans length scales from the system size $L$ to the healing length $\xi$, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when $L \gg \xi$. We present a matrix…
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…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…
The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the phase space of tensor-valued conductivity and position in…
In this work, we tackle the resolution of partial differential equations (PDEs) on digital quantum computers. Two fundamental PDEs are addressed: the anisotropic diffusion equation and the anisotropic convection equation. We present a…
Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases.…
We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…