Abstract: In this talk, I will introduce a new measurement-based model of quantum computation. This model relies on a new class of quantum error-correcting codes that we call dynamic automorphism (DA) codes, which generalize the recently developed Floquet codes. DA codes operate through a sequence of anti-commuting measurements that encode logical information and collect error syndromes, while simultaneously applying logical gates by implementing automorphisms of a certain anyon theory. 

The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and rarely three-qubit measurements. Using adaptive two-qubit measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model. 

The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].