Title: Floquet codes, TQFTs, automorphisms, and quantum computation
Speaker: Nathanan Tantivasadakarn (Cal Tech)
Abstract: Topological quantum error-correcting (QEC) codes such as the toric code have a deep connection to topological quantum field theory (TQFT). The recently introduced Floquet codes are implemented by a sequence of anticommuting measurements, causing the encoded information to be toggled between various subspaces at different times. This unusual property raises the question of whether it is possible to understand Floquet codes using TQFTs.
I will review a recent interpretation that these anticommuting measurements are the lattice counterpart of anyon condensation. Using this understanding, I will propose a generalization of Floquet codes called dynamic automorphism (DA) codes, that not only encodes quantum information, but can also simultaneously perform quantum computation.
From the lens of TQFT, the quantum computation can be understood as a sequence of time-like domain walls that implements automorphisms in a TQFT. The preservation of encoded information corresponds to the invertibility of the domain wall, and I will describe how to efficiently compute automorphisms from a sequence of condensations. I will further show that these sequences of condensations in a particular 2+1D TQFT with boundaries is sufficient to implement the full Clifford group of logical gates in the corresponding code. A similar setup in a 3+1D TQFT allows us to implement a non-Clifford gate, making the first step towards a new measurement-based model of universal quantum computation.
URL associated with Seminar: https://www.asc.ohio-state.edu/math/vqss/
