Related papers: Automatic code generator for higher order integrat…

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…

This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…

We present pySecDec, a new version of the program SecDec, which performs the factorisation of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of…

We present a modular analysis program written in Python devoted to the estimation of autocorrelation times for Monte Carlo simulations by means of the $\Gamma$-method algorithm. We give a brief review of this method and describe the main…

Analytical nuclear gradients for fully internally contracted complete active space second-order perturbation theory (CASPT2) are reported. This implementation has been realized by an automated code generator that can handle spin-free…

Domain Large Language Models (LLMs) are developed for domain-specific tasks based on general LLMs. But it still requires professional knowledge to facilitate the expertise for some domain-specific tasks. In this paper, we investigate into…

We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…

We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…

Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these…

We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…

We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a…

Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…

Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…

We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in…

The standard hybrid Monte Carlo algorithm uses the second order integrator at the molecular dynamics step. This choice of the integrator is not always the best. Using the Wilson fermion action, we study the performance of the hybrid Monte…

This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…

Automated insight generation is a common tactic for helping knowledge workers, such as data scientists, to quickly understand the potential value of new and unfamiliar data. Unfortunately, automated insights produced by large-language…

We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…

Effective Hamiltonian calculations for large quantum systems can be both analytically intractable and numerically expensive using standard techniques. In this manuscript, we present numerical techniques inspired by Nonperturbative…