A large class of gapped phases of matter can be described by topological finite group gauge
theories. In this paper, we show how such gauge theories possess a higher-group global …

D topological phases of matter can host a broad class of non-trivial topological defects of
codimension-1, 2, and 3, of which the well-known point charges and flux loops are special …

We investigate topological order on fractal geometries embedded in n dimensions. We
consider the n-dimensional lattice with holes at all length scales the corresponding fractal …

The color code is both an interesting example of an exactly solved topologically ordered
phase of matter and also among the most promising candidate models to realize fault …

One of the leading quantum computing architectures is based on the two-dimensional (2D)
surface code. This code has many advantageous properties such as a high error threshold …

We study parallel fault-tolerant quantum computing for families of homological quantum low-
density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant …

We consider the Z 2 toric code, surface code, and Floquet code defined on a nonorientable
surface, which can be considered as families of codes extending Shor's nine-qubit code. We …

Fault-tolerant logic gates will consume a large proportion of the resources of a two-
dimensional quantum computing architecture. Here we show how to perform a fault-tolerant …

The quantum logic gates used in the design of a quantum computer should be both
universal, meaning arbitrary quantum computations can be performed, and fault-tolerant …

We study symmetry-enriched topological order in two-dimensional tensor network states by
using graded matrix product operator algebras to represent symmetry induced domain walls …