Related papers: Geometric and Algebraic Topological Methods in Qua…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
As a fundamental concept in condensed matter physics, quantum geometry within the Riemannian metric elucidates various exotic phenomena, including the Hall effects driven by Berry curvature and quantum metric. In this work, we propose novel…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of Bernstein-Vazirani and Grover. By combining the tools used in these algorithms--quantum fast transforms and amplitude…
We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…