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Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Computational codes based on the Diffusion Monte Carlo method can be used to determine the quantum state of two-electron systems confined by external potentials of various nature and geometry. In this work, we show how the application of…
A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…
A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
The computational demand posed by applying multi-Slater determinant trials in phaseless auxiliary-field quantum Monte Carlo methods (MSD-AFQMC) is particularly significant for molecules exhibiting strong correlations. Here, we propose using…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…