Quantum Matter Seminar
Speaker: Margarita Davydova (MIT)
Title: Floquet codes, automorphisms, and quantum computation
Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction. We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.
As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model. This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.
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-body measurements. Using adaptive two-body 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].