Related papers: Quantum isometry groups
Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…
We review the construction of the multiparametric inhomogeneous orthogonal quantum group ISO_qr(N) as a projection from SO_qr(N+2), and recall the conjugation that for N=4 leads to the quantum Poincare group. We study the properties of the…
This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
A survey of results on quantum Poincare groups and quantum Minkowski spaces is presented.
The analysis of papers on usage NMR in quantum computations is provided and the probable direction of the future investigations are considered.
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.
We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in \cite{qorient} has a $C^*$-action on the underlying $C^*$ algebra.
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 computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…
This is a PhD dissertation on the latest numerical quantum estimation schemes as of 2012, submitted to the National University of Singapore. The main content of the thesis focuses on accessing quantum information with informationally…
We present some informal remarks on aspects of relativistic quantum computing.
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…