Topological Subsystem Codes

TL;DR

This paper introduces a new family of 2D topological subsystem quantum error-correcting codes with efficient syndrome measurement, explores their boundary properties, and links classical statistical models to optimal error correction under depolarizing noise.

Contribution

It presents a novel class of 2D topological subsystem codes, analyzes their boundary limitations, and establishes a mapping to classical models for improved error correction.

Findings

2-local Pauli operators suffice for syndrome measurement

Boundaries cannot be introduced in the usual way

Mapping to classical models enables optimal error correction

Abstract

We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational power of code deformation in these codes, and show that boundaries cannot be introduced in the usual way. In addition, we give a general mapping connecting suitable classical statistical mechanical models to optimal error correction in subsystem stabilizer codes that suffer from depolarizing noise.