A mathematical quantisation of a Random Access Memory (RAM) is proposed starting from its matrix representation. This quantum RAM (q-RAM) is employed as the neural unit of q-RAM-based Neural Networks, q-RbNN, which can be seen as the quantisation of the corresponding RAM-based ones. The models proposed here are direct realisable in quantum circuits, have a natural adaptation of the classical le...

Abstract In this paper, we explore a recently emerged approach to the problem of quantisation based on notion ideals. We explicitly prove that nonabelian Volterra together with whole hierarchy its symmetries admits deformation quantisation. show all odd-degree admit also non-deformation discuss for periodic including their quantum Hamiltonians, central elements quantised algebras, and demonstra...

Motivated by the success of classical random walks and chaotic dynamical systems, we study the quantisation of the random walk over Z and its relationships with a classical chaotic system x → 2xmod1, x ∈ [0,1]. In the physics literature, quantum random walks have been studied, for instance, by Ambainis et al. [1] and Konno et al. [8, 9]. In [8], Konno shows that the quantum random walk over Z c...

A formulation of quantum mechanics with additive and multiplicative (q-) difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding quantisation method. After a short discussion this method is translated step-by-step to a framework based on difference operators. To restrict the resulting plethora ...

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the fi...

In this report various aspects of Finite Temperature and Density Quantum Field Theory are discussed. The main point being the calculation of Green’s functions in this context, in which pertubation theory is used. The motivation for calculating Green’s functions comes from their wide application in modern Physics. The techniques that are presented here are used in such areas as condensed matter,...

The present work is addressed to defects and boundaries in quantum field theory considering the application to AdS/CFT correspondence. We examine interactions of fermions with spins localised on these boundaries. Therefore, an algebra method is emphasised adding reflection and transmission terms to the canonical quantisation prescription. This method has already been applied to bosons in two sp...