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We show that the correspondence between quantum and classical mechanics can be tuned by varying the coupling strength between the cavity modes and an atom or a molecule. In the acceleration gauge the cavity-matter system is represented by…

In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of…

As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…

All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them…

Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…

Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…

In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…

We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega-theory, and are similar to other pseudo-analytic structures…

A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed…

This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…

Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…

We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer, a method we call variational coherent quantum annealing (VCQA). It involves optimizing the…

Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the…

Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation…

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…

Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such…

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…

I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and…

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

A new type of a nonlinear gauge quantum theory (superrelativity) has been proposed. Such theory demands a radical reconstruction of both the quantum field conception and spacetime structure, and this paves presumably way to the…