Related papers: Neural Projected Quantum Dynamics: a systematic st…
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of…
We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…
Computational methods both open the frontiers of economic analysis and serve as a bottleneck in what can be achieved. We are the first to study whether Quantum Monte Carlo (QMC) algorithm can improve the runtime of economic applications and…
Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real-…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, and yet it remains computationally expensive on classical computers. We have…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
We consider several issues related to the multidimensional integration using a network of heterogeneous computers. Based on these considerations, we develop a new general purpose scheme which can significantly reduce the time needed for…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to…
Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…
Sequential Monte Carlo methods are a powerful framework for approximating the posterior distribution of a state variable in a sequential manner. They provide an attractive way of analyzing dynamic systems in real-time, taking into account…
The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function…
We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyse the…
The quantum dynamics of open many-body systems poses a challenge for computational approaches. Here we develop a stochastic scheme based on the positive P phase-space representation to study the nonequilibrium dynamics of coupled spin-boson…