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We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory…
The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of…
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course,…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.
We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of…
We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…