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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J. Martin Lindsay, Adam G. Skalski (2005)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Maria Elvira Mancino (1994)
Rendiconti del Seminario Matematico della Università di Padova
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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...
Luigi. Accardi, M. Schürmann (1988)
Mathematische Zeitschrift
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(1998)
Banach Center Publications
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P. Ługiewicz, R. Olkiewicz (2006)
Banach Center Publications
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Kalyan B. Sinha (2006)
Banach Center Publications
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In the framework of the symmetric Fock space over L²(ℝ₊), the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied. Then this result is used to prove the strong convergence of a quantum random walk as a map from an initial algebra 𝓐 into 𝓐 ⊗ ℬ (Fock(L²(ℝ₊))) to a *-homomorphic quantum stochastic flow.
A. Barhoumi, H. Ouerdiane (2006)
Banach Center Publications
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We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.
Timothy Eyre (1998)
Banach Center Publications
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A brief introduction to -graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation df(Λ) = f(Λ + dΛ) - f(Λ) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of -graded quantum stochastic calculus.
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...
Ayoola, E.O., Adeyeye, John O. (2007)
Journal of Applied Mathematics and Stochastic Analysis
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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...