Related papers: Recent Developments in Real Quantifier Elimination…
We present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets…
Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving…
Several quantum algorithms for linear algebra problems, and in particular quantum machine learning problems, have been "dequantized" in the past few years. These dequantization results typically hold when classical algorithms can access the…
Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…
Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent…
This article provides an introduction to and review of the field of computer-aided molecular design (CAMD). It is intended to be approachable for the absolute beginner as well as useful to the seasoned CAMD practitioner. We begin by…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose…
Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of…
Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems…
Typically, a practical algorithm of hardware verification obtains a semantic result by being applied to a particular formula $F$. That is, although this algorithm uses the specifics of $F$ (sometimes inadvertently), its result holds for all…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
Recent advancements in quantum computing (QC) and machine learning (ML) have fueled significant research efforts aimed at integrating these two transformative technologies. Quantum machine learning (QML), an emerging interdisciplinary…
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…
Modern software systems complexity challenges efficient testing, as traditional machine learning (ML) struggles with large test suites. This research presents a hybrid framework integrating Quantum Annealing with ML to optimize test case…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs,…
Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction…