Related papers: Computable functions, quantum measurements, and qu…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
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…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
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…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system.…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We raise the possibility of developing a theory of constructing quantum dynamical observables independent from quantization and deriving classical dynamical observables from pure quantum mechanical consideration. We do so by giving a…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
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…
We study the limitations of deterministic programmability of quantum circuits, e.g., quantum computer. More precisely, we analyse the programming of quantum observables and channels via quantum multimeters. We show that the programming…
"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…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…