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We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model…
Algorithms and hardware for solving quadratic unconstrained binary optimization (QUBO) problems have made significant recent progress. This advancement has focused attention on formulating combinatorial optimization problems as quadratic…
In this paper, we propose an efficient numerical approach for solving a specific type of quartic inhomogeneous polynomial optimization problem inspired by practical applications. The primary contribution of this work lies in establishing an…
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
Optimizing objective functions stands to benefit significantly from leveraging quantum computers, promising enhanced solution quality across various application domains in the future. However, harnessing the potential of quantum solvers…
In this paper we develop a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid…
We introduce kernel-QA, a black-box optimization (BBO) method that constructs surrogate models analytically using low-order polynomial kernels within a quadratic unconstrained binary optimization (QUBO) framework, enabling efficient…
The increasing complexity of industrial scheduling and transport routing problems motivates the study of alternative optimization formulations and computational paradigms. In this work, we study how higher-order unconstrained binary…
There is a growing interest in harnessing the potential of the Rydberg-atom system to address complex combinatorial optimization challenges. Here we present an experimental demonstration of how the quadratic unconstrained binary…
We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments…
The feedback-based algorithm for quantum optimization (FALQON) has recently been proposed to solve quadratic unconstrained binary optimization problems. This paper efficiently generalizes FALQON to tackle quadratic constrained binary…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
This paper discusses a class of two-block smooth large-scale optimization problems with both linear equality and linear inequality constraints, which have a wide range of applications, such as economic power dispatch, data mining, signal…