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A hypergraph is a natural generalization of a graph, where an edge (often called hyperedge) can simultaneously connect any number of vertices. The fact that hyperedges can connect more than two vertices facilitates a more faithful representation of many real-world networks. For example, given a set of proteins and a set of protein complexes, the corresponding hypergraph naturally captures the information on proteins that interact together within a protein complex. For a biochemical reaction system, the hypergraph representation indicates which biomolecules participate in a particular reaction. Collaboration networks can also be represented by a hypergraph, where vertices represent individuals and hyperedges connect individuals who were involved in a specific collaboration, e.g. a scientific paper, a patent, a consulting task, or an art performance.

The core of a graph - defined as the remainder of the greedy leaf removal procedure where leaves (vertices of degree one) and their neighbors are removed iteratively from the graph - has been related to the conductor-insulator transition, structural controllability, and many combinatorial optimization problems. In fact, the size of the core is related to a fundamental combinatorial issue: the computational complexity of the minimum vertex cover (MVC) problem. The MVC aims to find the smallest set of vertices in a graph (or hypergraph) so that every edge (or hyperedge) is incident to at least one node in the set.

I will talk about two generalizations of the core in graphs to hypergraphs, one associated with the edge-cover problem and another associated with the vertex-cover problem. We found that these two cores tend to be very small in real-world hypergraphs. This result indicates that the hyperedge and vertex cover problems in real-world hypergraphs can actually be solved in polynomial time.

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Single molecule techniques have the potential to reveal information about excitation energy transfer processes in complex multi chromophoric systems.

In this seminar talk I will present the application of low temperature, plasmonic and ultrafast femtosecond pulse shaping single molecule spectroscopy techniques, that are able to advance the understanding of energy transfer processes in photosynthetic pigment protein complexes.

The results point towards the importance of quantum biology in photosynthesis.

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Sometimes it is more convenient to store excess energy in a small region of space rather than spreading it over all the available volume. This may happen when the evolution of a system is characterized by additional dynamic constraints that promote energy localization for entropic reasons.

In this seminar I will discuss the role of peculiar nonlinear excitations (discrete breathers) for the localization process in networks of coupled oscillators.

Particular attention will be devoted to the dynamics of a Discrete Nonlinear Schroedinger Equation which exhibits a metastable phase with a finite density of breathers and partial energy localization.

Such state persists over very long (astronomical) times as a consequence of the extremely low interaction of these excitations with the surrounding background.

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Over the past 30 years, two different computational paradigms have been developed based on the premise that the laws of quantum mechanics could provide radically new and more powerful methods of information processing. One of these approaches is to encode the solution of a computational problem into the ground state of a programmable many-body quantum Hamiltonian system. Although, there is empirical evidence for quantum enhancement in certain problem instances, there is not a full theoretical understanding of the conditions for quantum speed up for problems of practical interest, especially hard combinatorial optimization and inference tasks in machine learning. In his talk, I will provide an overview of quantum computing paradigms and discuss the progress at the Google Quantum Artificial Intelligence Lab towards developing the general theory and overcoming practical limitations. Furthermore, I will briefly discuss two recent quantum machine learning primitives that we have developed known as Quantum Principal Component Analysis and Multiqubit Quantum Tunneling.

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Open quantum systems (OQS) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. In this talk I will give an overview of some recent advances to tackle the dynamics of an OQS beyond the Markov approximation, with special emphasis in hierarchy-based [1,2] and chain mapping-based [3] approaches. In the latter context, I will discuss the use of a thermofield transformation to describe thermal environments [4].

[1] Y. Tanimura. PRA, 41, 6676–6687 (1990).

[2] I. de Vega, J. Phys. A: Math. Theor. 48, 145202 (2015).

[3] A. W. Chin, J. Prior, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 107, 160601 (2011).

[4] I. de Vega and M.C. Bañuls, arXiv:1504.07228.

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Maxwell’s demon was born in 1867 and his sole function was to illustrate some potential problems with the Second Law of thermodynamics. He still thrives in modern physics and plays an important role in clarifying connections between thermodynamics and information theory. In my talk I will present a variety of different demons which, when restricted by the Second Law, will lead to interesting consequences in electromagnetism, optics, gravity, quantum mechanics as well as quantum information. Finally, I will speculate if the concept of information could in some sense be considered deeper than the entities typically though of as fundamental in physics and will mention various efforts to derive quantum physics from simpler information theoretic axioms.

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Using the operational framework of completely positive, trace preserving operations and thermodynamic fluctuation relations, I will derive a lower bound for the heat exchange in a Landauer erasure process on a quantum system. The bound comes from a non-phenomenological derivation of the Landauer principle which holds for generic non-equilibrium dynamics. Furthermore the bound depends on the non-unitality of dynamics, giving it a physical significance that differs from other derivations. I will illustrate the framework to the model of a spin-1/2 system coupled to an interacting spin chain at finite temperature.

I will further investigate the link between information and thermodynamics embodied by Landauer principle in an open-system dynamics embodied by a collision-based mechanism involving a suitable multipartite system and a multi-particle spin reservoir at finite temperature. I will demonstrate that Landauer principle holds, in such an open configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system, Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. I will illustrate such principle using two paradigmatic cases.

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Starting from the birth of statistical mechanics, the linkage between thermodynamics and information is a field alive with many discussions and a large variety of (discording) interpretations. The most accepted framework is the one formulated by Bennett which states a one-to-one relationship between thermodynamic and logic reversibility. In this talk, critical failures of this relationship are analyzed by using arguments taken from recent papers by Sagawa. In particular it will be proven that thermodynamic entropy and information are not interchangeable. Some other critical points of Bennett claims will also be presented as the basic ideas behind an experiment now performed in Perugia.

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