Abstract We construct (2+ 1)-dimensional lattice systems, which we call fusion surface
models. These models have finite non-invertible symmetries described by general fusion 2 …

A bstract Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that
its one-form symmetry defects have nontrivial braiding, namely they are charged under the …

In the Standard Model, some combination of the baryon B and lepton L number symmetry is
free of mixed anomalies with strong and electroweak su (3)× su (2)× u (1) Y˜ gauge forces …

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 …

Despite growing interest in beyond-group symmetries in quantum condensed matter
systems, there are relatively few microscopic lattice models explicitly realizing these …

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 develop a systematic theory of symmetry fractionalization for fermionic topological
phases of matter in (2+ 1) D with a general fermionic symmetry group G f. In general, G f is a …

In this paper, we derive the explicit formula for higher cup products on hypercubic lattices
based on the recently developed geometrical interpretation on the simplicial complexes. We …

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 …

Two-dimensional topologically ordered states such as fractional quantum Hall fluids host
anyonic excitations, which are relevant for realizing fault-tolerant topological quantum …