Related papers: Adaptive Finite State Projection with Quantile-Bas…
In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
Large Language Models (LLMs) with chain-of-thought (COT) prompting have demonstrated impressive abilities on simple nature language inference tasks. However, they tend to perform poorly on Multi-hop Question Answering (MHQA) tasks due to…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
This work aims to address the problem of long-term dynamic forecasting in complex environments where data are noisy and irregularly sampled. While recent studies have introduced some methods to improve prediction performance, these…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…
Finite state machines (FSMs) are a theoretically and practically important model of computation. We propose a general, thermodynamically consistent model of FSMs and characterise the resource requirements of these machines. We model FSMs as…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…
We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lov\'asz local lemma, where each constraint is violated by a small number of…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends…
We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization…
We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…
Efficiently solving the Fokker-Planck equation (FPE) is crucial for understanding the probabilistic evolution of stochastic particles in dynamical systems, however, analytical solutions or density functions are only attainable in specific…
We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term…
Finite size scaling for the Schr\"{o}dinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using…