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We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We…
Machine learning has been increasingly utilized in the field of biomedical research to accelerate the drug discovery process. In recent years, the emergence of quantum computing has been followed by extensive exploration of quantum machine…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
The increasing amount of data processed on edge and the demand for reducing the energy consumption for large neural network architectures have initiated the transition from traditional von Neumann architectures towards in-memory computing…
Semidefinite programming (SDP) provides a powerful relaxation for the maximum cut problem. For a graph with rational weights, the decision problem of whether the SDP relaxation for the maximum cut problem is exact is known to be $NP$-hard;…
Efficient compression of language model weights is increasingly critical as model scale and deployment grow. Yet, most existing methods rely on handcrafted transforms and heuristics, reflecting the limited understanding of weights as a data…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
Quantum reservoir computing has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we…
We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by D the largest absolute value of the subdeterminants of the constraint matrix. In this paper we…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems. In a QCQP, we are asked to minimize a (possibly nonconvex) quadratic function subject to a number of (possibly nonconvex) quadratic…
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast…
Quantum reservoir computing (QRC) is a hardware-implementation-friendly quantum neural network scheme with minimal physical system requirements and a proven advantage over classical counterparts. We use an extension of the positive-P phase…
Computing-in-Memory architectures based on non-volatile emerging memories have demonstrated great potential for deep neural network (DNN) acceleration thanks to their high energy efficiency. However, these emerging devices can suffer from…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of…