Related papers: Photonic quantum algorithm for Monte Carlo integra…
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…
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…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
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…
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…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
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…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is…
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…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…