Related papers: Non-Orthomodular Models for Both Quantum Logic and…
In this short note we relate some known properties of propositional calculus to purely algebraic considerations of a Boolean algebra. Classes of formulas of propositional calculus are considered as elements of a Boolean algebra. As such…
Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical…
The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative…
We explore the logarithmic terms in the soft theorem in four dimensions by analyzing classical scattering with generic incoming and outgoing states and one loop quantum scattering amplitudes. The classical and quantum results are consistent…
The (meta)logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics more than sixty years ago. The major difference between Boolean…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
In this article we demonstrate the applications of classical and quantum machine learning in quantum transport and spintronics. With the help of a two-terminal device with magnetic impurity we show how machine learning algorithms can…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…