Related papers: The Garden of Quantum Spheres
We describe the quantum subspaces of Banica-Goswami's half-liberated real-spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.
We give a new representation of Euclidean quantum fields as scaling limits of systems of interacting, continuous, classical particles in the grand canonical ensemble.
Generalizing the octahedral configuration of six congruent cylinders touching the unit sphere, we exhibit configurations of congruent cylinders associated to a pair of dual Platonic bodies.
Factorization into spheres is achieved for skeleta of the simplex, cube, and cross-polytope, both explicitly and using Keevash's proof of existence of designs.
Far from being just a 2-level Quantum system the Qubit is a Unit Quaternion, also known as a Spinor. Therefore it follows that the Qubit is a 4-dimensional vector which traces a path on the surface of the unit 3-sphere. This is the meaning…
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so,…
The different large $N$ limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. We distinguish between the planar limit of SQCD theories, the M-theory limit suited in three and five dimensions, and…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
On the basis that the universe is a closed quantum system with no external observers, we propose a paradigm in which the universe jumps through a series of stages. Each stage is defined by a quantum state, an information content, and rules…
Quantum computers, if fully realized, promise to be a revolutionary technology. As a result, quantum computing has become one of the hottest areas of research in the last few years. Much effort is being applied at all levels of the system…
Some recent developments in the theory of quantum spin systems are reviewed.
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
In this talk, we give a glimpse of the problems with quantum gravity and some possible solutions.
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare…
The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…
We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground state is a universal resource for measurement based quantum…
We formulate quantum theory taking as a starting point the cone of states.