Quantum Information Seminar | September 30, 16:00
From Pauli Strings to Quantum Dynamics: A Unified Characterization
Understanding dynamical properties of quantum systems is a crucial task in quantum physics, from quantum information to many-body physics. This perspective has become especially useful for variational quantum algorithms, where dynamical properties characterize trainability, expressivity and reachability. In this talk I will discuss the case of dynamics generated by Pauli strings, for which we find an efficient algorithm capable of classifying the dynamical class and the Pauli orbits. The results follow from an insight relating Pauli commutators and transvections, a basic Clifford operation. This connection allows us to take advantage of a rich literature on transvection groups and graph theory. We then apply these tools to various settings, which allows us to characterize the dynamical properties of structured Pauli architectures, provide Clifford 3-designs for Pauli Lie groups and determine the symmetry properties of certain locally interacting many-body systems.
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Contact: Markus Heinrich