Related papers: Fusing the coordinates of quantum superspace
Cartan calculi on the extended quantum superplane are given. To this end, the noncommutative differential calculus on the extended quantum superplane is extended by introducing inner derivations and Lie derivatives.
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
In my talk I will present an overview of our recent work involving the use of supersymmetric quantum mechanics (SUSY-QM). I begin by discussing the mathematical underpinnings of SUSY-QM and then discuss how we have used this for developing…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…
A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the \emph{double-graded quantum superplane}. The commutation…
A non-commutative differential calculus on the $h$-superplane is presented via a contraction of the $q$-superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the $(1+1)$…
The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results…
Quantum computing provides a novel approach to addressing conventionally intractable issues in large-scale optimization. Space logistics missions require the efficient routing of payloads, spacecraft, and resources across complex networks,…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
We show the Standard Model and SuperString Theories can be naturally based on a Quantum Computer foundation. The Standard Model of elementary particles can be viewed as defining a Quantum Computer Grammar and language. A Quantum Computer in…
The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As…
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the…
This paper is a collection of lecture notes on the superfield approach in three- and four-dimensional supersymmetric quantum field theory. Many examples of the applications of this approach to different superfield models are considered.
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Quantum computing, leveraging the principles of quantum mechanics, has been found to significantly enhance computational capabilities in principle, in some cases beyond classical computing limits. This paper explores quantum computing's…