12:00 pm 3r Floor Atrium
Floquet codes, TQFTs, automorphisms, and quantum computation.
Topological quantum error-correcting codes (QEC) such as the toric code have a deep connection to topological quantum field theory (TQFT). On the other hand, a recently proposed QEC called Floquet codes are implemented by a sequence of anticommuting measurements, causing the encoded information to be toggled between various subspaces at different times. This raises the question of whether it is possible to understand Floquet codes using TQFTs.
I will review a recent interpretation that these anticommuting measurements can be viewed as condensations of anyons that braid non-trivially. Using this understanding, I will propose a generalization of Floquet codes which we call 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 in this model can be understood as a sequence of time-like domain walls that implements automorphisms in a TQFT. The preservation of logical information corresponds to transparency of the domain wall, and I will describe how to efficiently compute automorphisms from a sequence of condensations. I will further show that a set of condensation sequences 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 universal quantum computation using measurements only.