Related papers: A Geometric Algebra Perspective On Quantum Computa…
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
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…
The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Recently de La Torre et al. [1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result…
Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients, isomorphic $\mathcal{G}_{1,4}$. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The…
Unitary gates with high entangling capabilities are relevant for several quantum-enhanced technologies. For symmetric multiqubit systems, such as spin states or bosonic systems, the particle exchange symmetry restricts these gates and also…
We comment on structural properties of the algebras $\mathfrak{A}_{LQG/LQC}$ underlying loop quantum gravity and loop quantum cosmology, especially the representation theory, relating the appearance of the (dynamically induced)…
The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…