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Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes…
Large Language Models (LLMs) are versatile and demonstrate impressive generalization ability by mining and learning information from extensive unlabeled text. However, they still exhibit reasoning mistakes, often stemming from knowledge…
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
Definition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on…
In this paper, we study semi-supervised Handwritten Mathematical Expression Recognition (HMER) via exploring both labeled data and extra unlabeled data. We propose a novel consistency regularization framework, termed SemiHMER, which…
This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Image Difference Captioning (IDC) generates natural language descriptions that precisely identify differences between two images, serving as a key benchmark for fine-grained change perception, cross-modal reasoning, and image editing data…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in…
Navigating the complexities of physics reasoning has long been a difficult task for Large Language Models (LLMs), requiring a synthesis of profound conceptual understanding and adept problem-solving techniques. In this study, we investigate…
Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations…
p$^\dagger$q is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and to realize proof-of-concept implementations of these equations for rapid prototyping. Central to this library is a…
Molecular representations are of fundamental importance for the modeling and analysis of molecular systems. Representation models and in general approaches based on topological data analysis (TDA) have demonstrated great success in various…