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Displaying similar documents to “The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}”

Dirac operator on the standard Podleś quantum sphere

Ludwik Dąbrowski, Andrzej Sitarz (2003)

Banach Center Publications

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Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.

Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Elmar Wagner (2011)

Banach Center Publications

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It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2)...

An introduction to quantum annealing

Diego de Falco, Dario Tamascelli (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum...

An introduction to quantum annealing

Diego de Falco, Dario Tamascelli (2011)

RAIRO - Theoretical Informatics and Applications

Similarity:

Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum...

When is a quantum space not a group?

Piotr Mikołaj Sołtan (2010)

Banach Center Publications

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We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as...