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At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…
Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…
On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Computation is an input-output process, where a program encoding a problem to be solved is inserted into a machine that outputs a solution. Quantum computation conventionally relies on classical, external control outside the quantum…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such…
In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
Notwithstanding interest and excitement building around quantum computing in the last decades, a concise statement saying where this computing can truly help is still missing. As it is shown in the present paper, equal cost of computation…