Related papers: Quantum algorithms for uncertainty quantification:…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generalized solutions. Dissipative measure-valued solutions have been…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
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…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Anomaly detection plays a critical role in fraud detection, health care, intrusion detection, military surveillance, etc. Anomaly detection algorithm based on density estimation (called ADDE algorithm) is one of widely used algorithms.…
A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class…
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…
We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with…
We present a novel uncertainty quantification approach for high-dimensional stochastic partial differential equations that reduces the computational cost of polynomial chaos methods by decomposing the computational domain into…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…