Quantum Cellular Automata and Quantum Field Theories
Thursday, 24 September 2026 at 2pm
Room 1B26, ENS Paris-Saclay, 4 Av. des Sciences, 91190 Gif-sur-Yvette
Abstract: This thesis studies Quantum Cellular Automata (QCAs) as discrete-spacetime, strictly local, and unitary models of quantum field theories, with a focus on lattice artifacts, their resolution, and the digital quantum simulation of gauge theories.
We extend the gauged-QCA framework to non-Abelian symmetries, building the first QCA model coupling (1+1)D Dirac fermions to an SU(2) Yang–Mills gauge field.
We show that existing (1+1)D and (3+1)D QED QCAs suffer from fermion doubling, and introduce a flavor-staggering-only method that resolves this while preserving chiral symmetry and circumventing the Nielsen–Ninomiya no-go theorem. We then derive a closed-form discrete-time propagator for the (1+1)D Dirac QCA and compute the two-point correlation function for the flavor-fixed model.
Applying the flavor-staggering method to the lattice Schwinger model, we construct a gauge-invariant axial charge, compute the chiral anomaly dynamically a lattice, and provide a geometric realization via a topological-insulator embedding.