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Chemical algorithms are statistical algorithms described and represented as chemical reaction networks. They are particularly attractive for traffic shaping and general control of network dynamics; they are analytically tractable, they…
The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when…
Quantitative chemistry is central to modern chemical research, yet the ability of large language models (LLMs) to perform its rigorous, step-by-step calculations remains underexplored. To fill this blank, we propose QCBench, a Quantitative…
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…
Chemical transport models (CTMs), which simulate air pollution transport, transformation, and removal, are computationally expensive, largely because of the computational intensity of the chemical mechanisms: systems of coupled differential…
Computational chemistry has become an indispensable tool for generating data and insights, pervading all branches of experimental chemistry. Its most central concept is the potential energy hypersurface, key to all chemistry and materials…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In these conference proceedings, we discuss quantum algorithms for the simulation of perturbative Quantum Chromodynamics (QCD) processes. In…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
The Chemical Reaction Networks (CRN) interpreted through the differential semantics, even when restricted to elementary reactions with mass action law kinetics, form a Turing-complete language. This means that any computable real function…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
The Extended Church-Turing Thesis (ECTT) posits that all effective information processing, including unbounded and non-uniform interactive computations, can be described in terms of interactive Turing machines with advice. Does this…
In recent years, conventional chemistry techniques have faced significant challenges due to their inherent limitations, struggling to cope with the increasing complexity and volume of data generated in contemporary research endeavors.…
We present QDK/Chemistry, a software toolkit for quantum chemistry workflows targeting quantum computers. The toolkit addresses a key challenge in the field: while quantum algorithms for chemistry have matured considerably, the…