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Entanglement loss properties and classical simulability of quantum many-body systems

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In this talk I will expose different results concerning the properties of quantum many-body systems: on the one hand, I will introduce the concept of fine-grained entanglement loss together with its relation with majorization relations along parameter flows and Renormalization Group flows. The machinery of Conformal Field Theory will allow us to derive very general analytical properties, and some examples -like the XY quantum spin chain- will also be considered. On the other hand, I will describe results concerning the classical simulability of quantum many-body systems by means of Matrix Product States. In particular, I will present an approximated classical simulation of a quantum algorithm by adiabatic evolution solving hard instances of an NP-Complete problem up to 100 qubits.