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The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
Path integral Monte Carlo (PIMC) simulations have become an important tool for the investigation of the statistical mechanics of quantum systems. I discuss some of the history of applying the Monte Carlo method to non-relativistic quantum…
Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is…
The author's presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity,…
We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among…
We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly-efficient update algorithm,…
We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…
Quantum Monte Carlo (QMC) techniques are widely used in a variety of scientific problems and much work has been dedicated to developing optimized algorithms that can accelerate QMC on standard processors (CPU). With the advent of various…
We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin…
The fourth industrial revolution and the digital transformation, commonly known as Industry 4.0, is exponentially progressing in recent years. Connected computers, devices, and intelligent machines communicate with each other and interact…
The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
We present an exact quantum Monte Carlo method for spin systems coupled to dissipative bosonic baths which makes use of nonlocal wormhole updates to simulate the retarded spin-flip interactions originating from an off-diagonal spin-boson…
This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and…
We investigate the performance of the hybrid Monte Carlo algorithm in updating non-trivial global topological structures. We find that the hybrid Monte Carlo algorithm has serious problems decorrelating the global topological charge. This…