Related papers: A quantum-information-theoretic complement to a ge…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of…
Today, people are looking forward to get an awesome computational power. This kind of desire can be answered by quantum computing. By adopting quantum mechanics theory, it can generate a very fast computation result. As known, quantum…
The expression of human art, and supposedly sentient art in general, is modulated by the available rendition, receiving and communication techniques. The components or instruments of these techniques ultimately exhibit a physical, in…
The manuscript [arXiv:2603.19208] proposes a physically motivated postulate to select the appropriate formulation of quantum theory over real Hilbert spaces, ruling out the theory considered in [Nature 600, 625-629 (2021)] in favour of the…
Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is…
Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. In this note, we propose 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…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
Turing's famous `machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach to computing with objects of any finite type. Both…
According to the Gottesman-Knill theorem, quantum algorithms which utilise only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states,…
As far as algorithmic thinking is bound by symbolic paper-and-pencil operations, the Church-Turing thesis appears to hold. But is physics, and even more so, is the human mind, bound by symbolic paper-and-pencil operations? What about the…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
Computer simulations allow us to explore non-perturbative phenomena in physics. This has the potential to help us understand quantum gravity. Finding a theory of quantum gravity is a hard problem, but in the last decades many promising and…
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough.…
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…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…