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The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
We generalize the Time-Dependent Variational Principle (TDVP) to dissipative systems using Monte Carlo methods, allowing the application of existing variational classes for pure states, such as Matrix Product States (MPS), to the simulation…
Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to…
Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a…
While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
Piecewise-deterministic Markov process (PDMP) samplers constitute a state-of-the-art Markov chain Monte Carlo paradigm in Bayesian computation, with examples including the zig-zag and bouncy particle sampler (bps). Recent work on the…
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling…
We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm…
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of…
We study one-dimensional (1D) and two-dimensional (2D) Helium atoms using a new time-dependent quantum Monte Carlo (TDQMC) method. The TDQMC method employs random walkers, with a separate guiding wave attached to each walker. The ground…
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of…
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy…
Quantum Monte Carlo methods have proven to predict atomic and bulk properties of light and non-light elements with high accuracy. Here we report on the first variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking the…
The reliability of a complex industrial system can rarely be assessed analytically. As system failure is often a rare event, crude Monte-Carlo methods are prohibitively expensive from a computational point of view. In order to reduce…
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…