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Dynamical aspects of quantum information and classical simulability https://doi.org/10.17863/CAM.122018 Bejan, Mircea-Andrei Beri, Benjamin Quantum many-body dynamics describes how systems of interacting particles evolve, often giving rise to collective phenomena with no classical counterpart. Understanding these dynamical phases of matter is believed to be typically hard. To simulate such dynamics, we need to either emulate it on a quantum device—acting as a quantum simulator—or, by exploiting its underlying mathematical structure, find analytical solutions and efficient classical methods. This thesis explores how the dynamics of quantum information underpins complex quantum phenomena that can surpass classical simulability. In particular, we investigate when quantum simulators might be the most resource-efficient means of simulating quantum dynamics, and highlight dynamical phases that can be useful in benchmarking such devices. We first discuss phase transitions in classical simulability for systems evolving under unitary dynamics interspersed with measurements—key operations implemented on quantum simulators. Several quantum resources, including entanglement and magic, are believed to be necessary for quantum computational advantage. While entanglement dynamics and its phase transitions induced by the frequency of measurements have been extensively studied recently, here we mainly focus on classifying dynamical phases in terms of magic. Through analytical arguments and numerical experiments, we find distinct measurement-induced phase transitions in magic, entanglement, and simulability (either by stabiliser or tensor networks methods). Notably, we unveil robust dynamical phases which are low in magic—and thus efficiently classically simulable—despite being highly entangled. We then consider, in a classically simulable (free-fermionic) setup, a deep form of thermalisation. Conventional quantum thermalisation asks whether, at late times under unitary dynamics, a small subsystem's physical observables attain thermal expectation values. However, current quantum simulators enable access to the entire system and the correlations between subsystems. By leveraging such correlations, we rigorously demonstrate that, across an ensemble of states corresponding to all possible experimental snapshots, the full probability distribution of observables becomes universal. Since free fermions are efficiently classically simulable, our results can be used to benchmark quantum simulators. Moreover, we argue that probing this phenomenon might be experimentally feasible for weakly interacting systems, despite the exponentially many possible snapshots, if the dynamics remains close to this free-fermionic regime. These findings enhance our understanding of classical simulation complexity, and offer insights into novel dynamical phases and the potential uses of quantum simulators. University of Cambridge 2025-05-31 Thesis Doctoral Doctor of Philosophy (PhD) eng EPSRC PhD Studentship 2606484 https://www.repository.cam.ac.uk/handle/1810/390469 https://www.repository.cam.ac.uk/bitstreams/80eb21b6-1150-4746-bb8b-ffb509ccb3bb/download 2dc58e4252097cdd1dfa48d05be67213 https://www.repository.cam.ac.uk/bitstreams/8ddf7f26-f0c6-48b1-b320-6e6cccf4c13e/download 87eda9de84448d1f82354d60eee3eb5f http://purl.org/NET/rdflicense/allrightsreserved Classical Simulability Quantum Information and Computation Quantum Physics Quantum Statistical Mechanics Quantum Thermalisation