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Quantum machine learning (QML) is a rapidly growing field that combines quantum computing principles with traditional machine learning. It seeks to revolutionize machine learning by harnessing the unique capabilities of quantum mechanics…
We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
The Copenhagen interpretation is critically considered. A number of ambiguities, inconsistencies and confusions are discussed. It is argued that it is possible to purge the interpretation so as to obtain a consistent and reasonable way to…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear…
The breakdown of Ehrenfest's theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we examined the conservation of the probability density, the…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
Disputes on the foundations of Quantum Mechanics often involve the conception of reality, without a clear definition on which aspect of this broad concept of reality one refers. We provide an overview of conceptions of reality in classical…
A definition of quantum mechanical work is introduced in this dissertation, preserving the mathematical structure of the Classical Mechanics concept of work without, however, in any way invoking the notion of trajectory. By use of Gaussian…
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…