Related papers: Fourth Order Diffusion Monte Carlo Algorithms for …
High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They…
The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the…
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
In this paper, we solve quantum many-body problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the 'effective potential' correction within the recently proposed time-dependent quantum Monte…
Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…
We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…