Related papers: Dynamics of Langevin Simulation
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time. In this paper we study the highly accurate numerical algorithm of the…
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian…
We investigate the application of efficient recursive numerical integration strategies to models in lattice gauge theory from quantum field theory. Given the coupling structure of the physics problems and the group structure within lattice…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
We present recent results on two attempts at understanding and utilizing large-scale simulations of magnetic materials. In the first study we consider massively parallel implementations on a Cray T3E of the n-fold way algorithm for…
Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is…
We have studied the scalar $\phi^4$-model in the symmetric phase and the non--compact $U(1)$ gauge theory on a momentum lattice using the Langevin equation for generating configurations. In the $\phi^4$-model we have analyzed the…
We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium…
We present updated results of dynamic stabilisation (DS) applied to complex Langevin simulations of QCD in the heavy-dense limit and with staggered quarks. We show that DS is able to keep the unitarity norm sufficiently small, which leads…
We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms.…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
In this PhD thesis, we apply a combination of Malliavin calculus and Stein's method in the framework of probability approximations. The specific problems we tackle with these methods are motivated by probabilistic models in cosmology (Part…
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…