Related papers: A quantum spectral method for simulating stochasti…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…
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…
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties of Volterra processes and reviewing existing numerical…
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Quantum computers have attracted much attention in recent years. This is because the development of the actual quantum machine is accelerating. Research on how to use quantum computers is active in the fields such as quantum chemistry and…
A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and…
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…