Pauli topological subsystem codes from Abelian anyon theories
Abstract
We construct Pauli topological subsystem codes characterized by arbitrary twodimensional Abelian anyon theories–this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of twodimensional Pauli topological subsystem codes to systems of compositedimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on fourdimensional qudits based on the Z4(1) anyon theory with degenerate braiding relations and the chiral semion theory–both of which cannot be captured by topological stabilizer codes. The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higherform symmetries.
 Publication:

Quantum
 Pub Date:
 October 2023
 DOI:
 10.22331/q202310121137
 arXiv:
 arXiv:2211.03798
 Bibcode:
 2023Quant...7.1137E
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 67 + 35 pages, single column format, v2 published version