Related papers: A rational approximation for efficient computation…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation…
In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
Proposals for near-term experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms,…
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…
We evaluate an adaptive gaussian quadrature integration scheme that will be suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for "full non-LTE" radiation…
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
We consider the problem of efficiently computing the Uhlmann fidelity in the case when explicit density matrix descriptions are available. We derive an alternative formula which is simpler to evaluate numerically, saving a factor of 10 in…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
This paper presents a novel method of approximating the scalar Wiener-Hopf equation; and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds.…