@misc{aasen2022adiabatic,
author = {Aasen, David and Wang, Zhenghan and Hastings, Matthew},
title = {Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes},
howpublished = {arXiv},
year = {2022},
month = {April},
abstract = {The recent “honeycomb code” is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians and we give a conjectured description of the fundamental group and second and third homotopy groups of this space in two spatial dimensions. A single cycle of such a path can implement some automorphism of the topological order of that Hamiltonian. We construct such paths for arbitrary automorphisms of two-dimensional doubled topological order. Then, realizing this in the case of the toric code, we turn this path back into a sequence of checks, constructing an automorphism code closely related to the honeycomb code.},
url = {http://approjects.co.za/?big=en-us/research/publication/adiabatic-paths-of-hamiltonians-symmetries-of-topological-order-and-automorphism-codes/},
}