Topological Phases of Discrete Unitary Dynamics

Explore the fascinating realm of topological phases in discrete unitary dynamics through this 48-minute lecture by Jeongwan Haah from PCS Institute for Basic Science. Delve into the concept of topological phases of matter, defined as equivalence classes of ground states in gapped Hamiltonian families, and their relation to local quantum circuits. Examine the analogous question for discrete time evolution operators on lattices, considering the impact of lattice translation and recent discoveries in higher spatial dimensions. Gain insights into the complete classification result in the Clifford category across all spatial dimensions, including its periodicity in higher dimensions and connection to the Witt group of prime fields. Follow the lecture's progression from the introduction and problem definition through key concepts such as Hamiltonian evolution, local operators, Clifford circuits, localized unitary dynamics, and the Local One Construction, culminating in a thought-provoking exploration of local unitary questions.