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Quantum computers are anticipated to transcend classical supercomputers for computationally intensive tasks by exploiting the principles of quantum mechanics. However, the capabilities of the current generation of quantum devices are…
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…
We prove the existence and uniqueness of solutions to a class of quadratic BSDE systems which we call triangular quadratic. Our results generalize several existing results about diagonally quadratic BSDEs in the non-Markovian setting. As…
The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum…
Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and…
In the article, we discuss the conservation laws for the nonlinear Schr\"{o}dinger equation with wave operator under multisymplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is…
In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…
This paper tackles the problem of constructing Bezout matrices for Newton polynomials in a basis-preserving approach that operates directly with the given Newton basis, thus avoiding the need for transformation from Newton basis to monomial…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
The extended Ising machine (EIM) enhances conventional Ising models, which handle only binary quadratic forms by allowing constraints through real-valued dependent variables. We address the quadratic knapsack problem (QKP), hard to solve…
In this paper we mainly propose efficient and reliable numerical algorithms for solving stochastic continuous-time algebraic Riccati equations (SCARE) typically arising from the differential statedependent Riccati equation technique from…
In this paper, combining the ideas of exponential integrators and discrete gradients, we propose and analyze a new structure-preserving exponential scheme for the conservative or dissipative system $\dot{y} = Q(M y + \nabla U (y))$, where…
Quadratic Unconstrained Binary Optimization (QUBO)-based suppression in object detection is known to have superiority to conventional Non-Maximum Suppression (NMS), especially for crowded scenes where NMS possibly suppresses the…
Reinforcement learning has traditionally been studied with exponential discounting or the average reward setup, mainly due to their mathematical tractability. However, such frameworks fall short of accurately capturing human behavior, which…
This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular…