Date: 4th April 2014 Venue: Welsh Room, Old College (Aberystwyth) Please note that the venue of the workshop is different from the location of the Department of Mathematics and Physics of Aberystwyth University (which is in Penglais Campus). Timetable 09.15 We meet in the Old College. 09.30-10.20 Zoltan Zimboras Representation theory and unitary quantum control 10.30-11.00 Daniel Burgarth Quantum Computing in Plato's Cave 11.00-11.30 Tea/Coffee 11.30-12.20 Michael Dritschel Completely bounded kernels 12.30-14.00 Lunch 14.00-14.50 Alexander Belton Construction and dilation of quantum dynamical semigroups 15.00-15.30 Michal Gnacik Evolutions of quantum systems via quantum stochastic calculus 15.30-16.00 Tea/Coffee 16.00-16.50 Robin Hillier Dynamical Decoupling After that, if the weather is nice, we can walk along the seaside before having dinner together. More details about the talks: Dr Alexander Belton Department of Mathematics and Statistics Lancaster University Title: Construction and dilation of quantum dynamical semigroups (joint work with Stephen Wills, University College Cork) Abstract: We will show how to use quantum-stochastic methods to construct certain strongly continuous quantum dynamical semigroups on C*-algebras. These are realised indirectly, as expectation semigroups of non-commutative Markov processes. The extra structure possessed by such processes, in particular the fact that they are composed of *-homomorphisms, allows existence to be established for semigroup generators which are unbounded but satisfy some regularity conditions. Dr Daniel Burgarth Department of Mathematics and Physics Aberystwyth University Title: Quantum Computing in Plato's Cave (joint work with Paolo Facchi, Vittorio Giovannetti, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa) Abstract: We show that mere observation of a quantum system can turn its dynamics from a very simple one into a universal quantum computation. This effect, which occurs if the system is regularly observed at short time intervals, can be rephrased as a modern version of Plato's Cave allegory. More precisely, while in the original version of the myth, the reality perceived within the Cave is described by the projected shadows of some more fundamental dynamics which is intrinsically more complex, we found that in the quantum world the situation changes drastically as the "projected" reality perceived through sequences of measurements can be more complex than the one that originated it. After discussing examples we go on to show that this effect is generally to be expected: almost any quantum dynamics will become universal once "observed" as outlined above. Conversely, we show that any complex quantum dynamics can be "purified" into a simpler one in larger dimensions. Dr Michael Dritschel School of Mathematics and Statistics Newcastle University Title: Completely bounded kernels (joint work with Tirtha Bhattacharyya and Chris Todd) Abstract: The so-called Kolmogorov decomposition is a well-known and useful tool in the study of positive scalar valued kernels. There have been various generalisations of this, ultimately ending in a version for completely positive kernels mapping into L(A,B), where A and B are C*-algebras, due to Barreto, Bhat, Liebscher and Skeide. The proof follows the familiar GNS-construction as in the proof of the Stinespring dilation theorem. In the course of another project we were working with certain L(A,B)-valued kernels which are differences of completely positive kernels, and the question naturally arose: are all Hermitean completely bounded kernels of this form? Indeed, is there something akin to the Wittstock theorems for completely bounded kernels? We found that under suitable restrictions, there is. This talk discusses what we discovered. Michal Gnacik Department of Mathematics and Statistics Lancaster University Title: Evolutions of quantum systems via quantum stochastic calculus (joint work with Alexander Belton and Martin Lindsay) Abstract: We introduce some quantum stochastic calculus techniques to describe the evolution between an open quantum system and a particle reservoir. We start with a discrete setup, for instance, when an electromagnetic field in a cavity is coupled to an infinite chain of atoms, which are shot, one by one through the cavity and interact with the cavity field. This phenomenon is modelled via repeated quantum interactions where a single interaction occurs during a short time interval of length h. We show that the continuous-time limit of the associated discrete-time unitary evolution forms a unitary quantum stochastic cocycle. Dr Robin Hillier Department of Mathematics and Statistics Lancaster University Title: Dynamical decoupling (joint work with Christian Arenz and Daniel Burgarth) Abstract: Random dynamical decoupling is a correction procedure aiming to stabilise quantum registers suffering dephasing. A nice mathematical description is obtained in terms of probability theory on Lie groups and UCP semigroups in finite dimensions. I will explain how all this works and what consequence we can draw about the physics of the quantum register and quantum mechanics in general. Dr Zoltan Zimboras University College London Title: Representation theory and unitary quantum control Abstract: Recently many results connected to higher-order symmetries and the representation theory of Lie algebras have appeared in the quantum control literature. In this talk, after reviewing some of the previous achievements, we report on our recent work in this field. By proving a new representation theoretic theorem, we have found an efficient algorithm to determine whether a unitary operation can be generated by a set of Hamiltonians or not. Interestingly, we can also show (using another theorem on finite groups) that a similar result for unitaries generated by a discrete set of gates cannot exist. Participants: Christian Arenz (cha24@aber.ac.uk) Alexander Belton (a.belton@lancaster.ac.uk) Roger Bliss (rsb5@aber.ac.uk) Daniel Burgarth (dkb3@aber.ac.uk) Michael Dritschel (michael.dritschel@ncl.ac.uk) Gwion Evans (dfe@aber.ac.uk) Michal Gnacik (m.gnacik1@lancaster.ac.uk) Rolf Gohm (rog@aber.ac.uk) John Gough (jug@aber.ac.uk) Robin Hillier (r.hillier@lancaster.ac.uk) Mateusz Jurczynski (mateusz.m.jurczynski@gmail.com) Alexander Pitchford (agp1@aber.ac.uk) Otgonbayar Uuye (UuyeO@cardiff.ac.uk) Zoltan Zimboras (zimboras@gmail.com) For further inquiries please contact Dr Rolf Gohm, email: rog@aber.ac.uk Department of Mathematics and Physics Aberystwyth University Aberystwyth SY23 3BZ UK |

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