Symmetrizing quantum dynamics beyond gossip-type algorithms

Recently, consensus-type problems have been formulated in the quantum domain. Obtaining average quantum consensus consists in the dynamical symmetrization of a multipartite quantum system while preserving the expectation of a given global observable. In this paper, two improved ways of obtaining consensus via dissipative engineering are introduced, which employ on quasi local preparation of mixtures of symmetric pure states, and show better performance in terms of purity dynamics with respect to existing algorithms. In addition, the first method can be used in combination with simple control resources in order to engineer pure Dicke states, while the second method guarantees a stronger type of consensus, namely single-measurement consensus. This implies that outcomes of local measurements on different subsystems are perfectly correlated when consensus is achieved. Both dynamics can be randomized and are suitable for feedback implementation.Comment: 11 pages, 3 figure

A Common Symmetrization Framework for Iterative (Linear) Maps

International audienceThis paper highlights some more examples of maps that follow a recently introduced " symmetrization " structure behind the average consensus algorithm. We review among others some generalized consensus settings and coordinate descent optimization

Symmetrizing dynamics: from classical to quantum applications

Among the issues regarding networked systems, the “consensus problem” and the related algorithms have received a significant share of attention during the last ten years. In this problem the network agents asymptotically have to attain agreement on the value of some objective variable under local communication constraints. A number of algorithms have been developed to address this problem, among which the celebrated gossip algorithm. The latter relays on switching dynamics and, under rather weak assumptions, exhibits robust convergence under variations in the interaction constraints, i.e. the network topology. In this dissertation we reinterpret the goal of the consensus problem as a symmetrisation problem, and we address it by a switching-type dynamics based on convex combinations of actions of a finite group. In order to study the convergence of our class of algorithms we lift the dynamics to an abstract, group-theoretic level that allow us to derive general conditions for convergence. Such conditions, in fact, are independent of the particular group action, and focus only on the group itself and the way the iterations are selected. Convergence is guaranteed provided that some mild assumptions on the selection rule for the iterations are fulfilled. Furthermore, this class of algorithms retains the robustness features and unsupervised character of the consensus algorithm. Our reformulation allow to devise algorithms for application as diverse as randomized discrete Fourier transform and random state generation. We pose a special emphasis on the extension of the consensus problem to the quantum domain. In this setting we highlight how, due to the richer mathematical structure over which the internal state is encoded, the definition of the consensus goal admits various extensions, each of them exhibiting different features. We also propose a suitable dissipative dynamics enacting the symmetrising gossip interactions and then use our general result on convergence to prove it ensures asymptotic convergence. Beside the technical results, one of the main contributions of our work is a new, generalized view point on consensus, which allows us to extend the robustness of consensus-inspired algorithms to new problems in apparently unrelated fields. This reinforces the role of consensus algorithms as fundamental tools for distributed computing, both in the classical and the quantum setting

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Development and Application of Chemometric Methods for Modelling Metabolic Spectral Profiles

The interpretation of metabolic information is crucial to understanding the functioning of a biological system. Latent information about the metabolic state of a sample can be acquired using analytical chemistry methods, which generate spectroscopic profiles. Thus, nuclear magnetic resonance spectroscopy and mass spectrometry techniques can be employed to generate vast amounts of highly complex data on the metabolic content of biofluids and tissue, and this thesis discusses ways to process, analyse and interpret these data successfully. The evaluation of J -resolved spectroscopy in magnetic resonance profiling and the statistical techniques required to extract maximum information from the projections of these spectra are studied. In particular, data processing is evaluated, and correlation and regression methods are investigated with respect to enhanced model interpretation and biomarker identification. Additionally, it is shown that non-linearities in metabonomic data can be effectively modelled with kernel-based orthogonal partial least squares, for which an automated optimisation of the kernel parameter with nested cross-validation is implemented. The interpretation of orthogonal variation and predictive ability enabled by this approach are demonstrated in regression and classification models for applications in toxicology and parasitology. Finally, the vast amount of data generated with mass spectrometry imaging is investigated in terms of data processing, and the benefits of applying multivariate techniques to these data are illustrated, especially in terms of interpretation and visualisation using colour-coding of images. The advantages of methods such as principal component analysis, self-organising maps and manifold learning over univariate analysis are highlighted. This body of work therefore demonstrates new means of increasing the amount of biochemical information that can be obtained from a given set of samples in biological applications using spectral profiling. Various analytical and statistical methods are investigated and illustrated with applications drawn from diverse biomedical areas