Quantum stochastic dynamics. I.
Majewski, Adam W., Zegarlinski, Boguslaw (1995)
Mathematical Physics Electronic Journal [electronic only]
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Majewski, Adam W., Zegarlinski, Boguslaw (1995)
Mathematical Physics Electronic Journal [electronic only]
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John Gough (2006)
Banach Center Publications
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We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.
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...
Diego de Falco, Dario Tamascelli (2011)
RAIRO - Theoretical Informatics and 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...
(1998)
Banach Center Publications
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Luigi. Accardi, M. Schürmann (1988)
Mathematische Zeitschrift
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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...
Nina V. Volosova (2010)
Banach Center Publications
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We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established,...
Viacheslav Belavkin, Matthew Brown (2011)
Banach Center Publications
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In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field , of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone...
Bishop, R.C., Bohm, A., Gadella, M. (2004)
Discrete Dynamics in Nature and Society
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