Related papers: On the Rayleigh-Ritz variational method
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
Strongly coupled quantum field theories in $(1+1)$ dimensions are notoriously hard to solve non-perturbatively. Variational methods, despite their success for quantum many-body physics on the lattice, have long lacked a natural ansatz…
Inspired by the recent work of Carleo and Troyer[1], we apply machine learning methods to quantum mechanics in this article. The radial basis function network in a discrete basis is used as the variational wavefunction for the ground state…
Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
We establish a simple method to assess the quantum Fisher information required for resolving two incoherent point sources with an imaging system. The resulting Cram\'er-Rao bound shows that the standard Rayleigh limit can be surpassed by…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. We solve the Schr\"odinger equation in terms of Weber functions and discuss the behavior of the eigenvalues and eigenfunctions. We derive the…
Quantum chemistry is one of the most promising applications of quantum computers in the near future. For noisy intermediate-scale quantum devices, the quantum-classical hybrid framework based on the variational quantum eigensolver (VQE) has…
Computing accurate yet efficient approximations to the solutions of the electronic Schr\"odinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of…
Using classical results of Rogers bounding the $L^2$-norm of Siegel transforms, we give bounds on the heights of approximate integral solutions of quadratic equations and error terms in the quantiative Oppenheim theorem of…
We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let $\phi : \tilde{C} \to C$ be an unramified morphism of non-singular plane projective curves defined over a number field $K$. We calculate an effective…
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce…
Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as…
In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…
This document is a pdf version of the series of blogposts about variational quantum algorithms (VQA) I originally posted on my blog Musty Thoughts. It provides an explanation of the basic variational algorithms, such as Variational Quantum…