相关论文: Numerical Algebraic Geometry for Energy Computatio…

To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods…

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…

In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…

We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Even though this problem is non-convex in the Euclidean sense…

Vladimir Arnold defined three invariants for generic planar immersions, i.e. planar curves whose self-intersections are all transverse double points. We use a variational approach to study these invariants by investigating a suitably…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

In this work, we propose a novel variational quantum approach for solving a class of nonlinear optimal control problems. Our approach integrates Dirac's canonical quantization of dynamical systems with the solution of the ground state of…

Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…

Using the embedded gradient vector field method we explicitly compute the list of critical points of the free energy for a Cosserat body model. We also formulate necessary and sufficient conditions for critical points in the abstract case…

In this work, we explore advanced machine learning techniques for minimizing Gibbs free energy in full 3D micromagnetic simulations. Building on Brown's bounds for magnetostatic self-energy, we revisit their application in the context of…

Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…

Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to…

This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…

We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy…

Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function),…

We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we…

Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…