Pumping Chirality in Three Dimensions - IPAM at UCLA

Explore a 50-minute lecture on "Pumping Chirality in Three Dimensions" presented by Matthew Hastings from Microsoft Research at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Delve into the complexities of bosonization, mapping fermions coupled to a Z_2 gauge field to a qubit system, and examine the non-trivial 3-fermion quantum cellular automaton (QCA). Investigate the relationship between framing-dependent phase and the pump of 8 copies of a p+ip state through the system. Uncover the resolution to an apparent paradox involving shallow depth circuits and non-trivial QCAs. Discuss the pump of fewer p+ip state copies and its impact on topologically degenerate ground states. Explore the implications for free Fermi evolution and non-trivial winding numbers in the context of the Brillouin Zone 3-torus and SU(Nb). Examine higher-dimensional generalizations of QCAs and their potential connections to Chern-Simons theory. Gain insights into cutting-edge research at the intersection of quantum physics, topology, and error correction.