Related papers: Circuits: An abstract viewpoint
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
Based on the foundational aspects which have been discussed as consequences of ongoing research on loop quantum gravity in the first part of this paper, the holistic aspects of the latter are discussed in this second part, aiming at a…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
We show that, on the abstraction level of quantum circuit diagrams, quantum circuit algorithms belong to the species of interactive sequential algorithms that we studied in earlier work. This observation leads to a natural specification…
How should we interpret physical theories, and especially quantum theory, if we drop the assumption that we should treat it as an exact description of the whole Universe? I expound and develop the claim that physics is about the study of…
In this note we construct a quantum Fourier transform circuit in a recursive way, by directly copying the 'divide and conquer' construction of the fast Fourier transform algorithm, rather than using the explicit formula that is given in…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
The development of quantum computing technologies builds on the unique features of quantum physics while borrowing familiar principles from the design of conventional devices. We introduce the fundamental concepts required for designing and…