4 research outputs found
Persistent homology analysis of a generalized Aubry-Andr\'{e}-Harper model
Observing critical phases in lattice models is challenging due to the need to
analyze the finite time or size scaling of observables. We study how the
computational topology technique of persistent homology can be used to
characterize phases of a generalized Aubry-Andr\'{e}-Harper model. The
persistent entropy and mean squared lifetime of features obtained using
persistent homology behave similarly to conventional measures (Shannon entropy
and inverse participation ratio) and can distinguish localized, extended, and
crticial phases. However, we find that the persistent entropy also clearly
distinguishes ordered from disordered regimes of the model. The persistent
homology approach can be applied to both the energy eigenstates and the
wavepacket propagation dynamics.Comment: Published version. 8 pages, 9 figure
Quantum Approaches to Data Science and Data Analytics
In this thesis are explored different research directions related to both the use of classical data analysis techniques for the study of quantum systems and the employment of quantum computing to speed up hard Machine Learning task
Persistent homology analysis of multiqubit entanglement
We introduce a homology-based technique for the classification of multiqubit state vectors with genuine entanglement. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown