Related papers: Test of variational approximation for $phi^4$ quan…
We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification.…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
We demonstrate the feasibility of performing sufficient configurational sampling of disordered oxides directly from first principles without resorting to the use of fitted models such as cluster expansion. This is achieved by harnessing the…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
Programmable quantum simulators based on Rydberg atom arrays are a fast-emerging quantum platform, bringing together long coherence times, high-fidelity operations, and large numbers of interacting qubits deterministically arranged in…
We outline the steps needed in to calibrate the Monte Carlo code in order to perform large scale simulations of real globular clusters. We calibrate the results against $N$-body simulations for $N = 2500$, 10000 and for the old open cluster…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
Monte Carlo simulation is an important tool for modeling highly nonlinear systems (like particle colliders and cellular membranes), and random, floating-point numbers are their fuel. These random samples are frequently generated via the…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…
Auxiliary-field quantum Monte Carlo (AFQMC) has repeatedly demonstrated itself as one of the most accurate quantum many-body methods, capable of simulating both real and model systems. In this article we investigate the application of AFQMC…
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons,…
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole…
QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We…
We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC,…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters…
We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large…
Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…