相关论文: Variational Estimates using a Discrete Variable Re…

The Pekeris coordinates provide a permutationally invariant set of coordinates for H$_3^+$. They are defined as linear combinations of the three internuclear distances that automatically fulfil the triangle inequality for all non-negative…

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…

Learning-based methods are promising to plan robot motion without performing extensive search, which is needed by many non-learning approaches. Recently, Value Iteration Networks (VINs) received much interest since---in contrast to standard…

Deep reinforcement learning (RL) algorithms suffer severe performance degradation when the interaction data is scarce, which limits their real-world application. Recently, visual representation learning has been shown to be effective and…

Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to…

Determining quantum excited states is crucial across physics and chemistry but presents significant challenges for variational methods, primarily due to the need to enforce orthogonality to lower-energy states, often requiring…

Pretrained Vision Transformers (ViTs) such as DINOv2 and MAE provide generic image features that can be applied to a variety of downstream tasks such as retrieval, classification, and segmentation. However, such representations tend to…

The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing…

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…

Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements…

This paper investigates the construction of deterministic matrices preserving the entropy of random vectors with a given probability distribution. In particular, it is shown that for random vectors having i.i.d. discrete components, this is…

Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the…

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this…

We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem…

A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…

A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is…

In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved…

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…