Related papers: The Quantum-Extended Church-Turing Thesis in Quant…
Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to…
The quantum-Extended Church-Turing thesis is a principle of physics as well as computer science. It asserts that the laws of physics will prevent the construction of a machine that can efficiently determine the results of any calculation…
The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of…
It is possible in principle to construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolution, would contradict the Church-Turing thesis, which lies at the…
There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in…
Roughly, the Church-Turing thesis is a hypothesis that describes exactly what can be computed by any real or feasible conceptual computing device. Generally speaking, the computational metaphor is the idea that everything, including the…
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is…
We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract…
We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies, and causes for misunderstanding, concerning the…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
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…
Two aspects of the physical side of the Church-Turing thesis are discussed. The first issue is a variant of the Eleatic argument against motion, dealing with Zeno squeezed time cycles of computers. The second argument reviews the issue of…
We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Practically measurable quantities resulting from quantum field theory are not described by hermitian operators, contradicting one of the cornerstone axioms of orthodox quantum theory. This could be a sign that some of the axioms of orthodox…
"Church's thesis" ($\mathsf{CT}$) as an axiom in constructive logic states that every total function of type $\mathbb{N} \to \mathbb{N}$ is computable, i.e. definable in a model of computation. $\mathsf{CT}$ is inconsistent in both…
Can a Turing Machine simulate the human mind? If the Church-Turing thesis is assumed to be true, then a Turing Machine should be able to simulate the human mind. In this paper, I challenge that assumption by providing strong mathematical…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…
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…