Related papers: Solving Major Problems Using Vector Affine Quantiz…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Enhanced quantization is an improved program for overcoming difficulties which may arise during an ordinary canonical quantization procedure. We review here how this program applies for a particle on circle.
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
A variation of the classic vector quantization problem is considered, in which the analog-to-digital (A2D) conversion is not constrained by the cardinality of the output but rather by the number of comparators available for quantization.…
In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
Quantization based techniques are the current state-of-the-art for scaling maximum inner product search to massive databases. Traditional approaches to quantization aim to minimize the reconstruction error of the database points. Based on…
Vector quantization is a technique in machine learning that discretizes continuous representations into a set of discrete vectors. It is widely employed in tokenizing data representations for large language models, diffusion models, and…
Vector Quantization (VQ) techniques face significant challenges in codebook utilization, limiting reconstruction fidelity in image modeling. We introduce a Dual Codebook mechanism that effectively addresses this limitation by partitioning…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
Neural networks have established as a generic and powerful means to approach challenging problems such as image classification, object detection or decision making. Their successful employment foots on an enormous demand of compute. The…
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantization of Convolutional Neural Networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the…
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in…
We develop a new method called affine facial reduction (FR) for recovering Slater's condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…