相关论文: Numerical Algebraic Geometry for Energy Computatio…

The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…

Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…

Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines,…

Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…

We revisit a classical problem in numerical linear algebra: given an $k$-dimensional subspace $\mathcal{Q}$ that approximates the leading eigenspace of an $n\times n$ positive semi-definite matrix $A$, the goal is to extract high-accuracy…

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…

Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present…

We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…

Many problems in computational science and engineering are simultaneously characterized by the following challenging issues: uncertainty, nonlinearity, nonstationarity and high dimensionality. Existing numerical techniques for such models…

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…

We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential…

Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…

This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system…

Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central…

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…

Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…

We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The…

Neural networks has recently attracted much interest as useful representations of quantum many body ground states, which might help address the infamous sign problem. Most attention was directed at their representability properties, while…

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph…

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…