Related papers: Unifying structures in quantum integrable systems
An overview of the quantum integrable systems (QIS) is presented. Basic concepts of the theory are highlighted stressing on the unifying algebraic properties, which not only helps to generate systematically the representative Lax operators…
A challenge in the theory of integrable systems is to show for every nonultralocal quantum integrable model, a possible connection to an ultralocal model. Some of such gauge connections were discovered earlier. We complete the task by…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
Advances in quantum information science (QIS) are providing transformative insights into the complexity of quantum many-body systems, potentially defining new frontiers in nuclear and high-energy physics. This review explores how…
Quantum Information Networks (QINs) attract increasing interest, as they enable connecting quantum devices over long distances, thus greatly enhancing their intrinsic computing, sensing, and security capabilities. The core mechanism of a…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded…
Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as…
Higher-dimensional quantum systems (qudits) offer advantages in information encoding, error resilience, and compact gate implementations, and naturally arise in platforms such as superconducting and solid-state systems. However, realistic…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…