Quantum codes on a lattice with boundary

TL;DR

This paper introduces a novel local-check additive quantum code on a 2D lattice with boundary, utilizing homology groups to describe logical operators, advancing quantum error correction techniques.

Contribution

It presents a new quantum code with boundary conditions, linking stabilizer operators to lattice faces and vertices, and employs homology for logical operator description.

Findings

New quantum code with boundary conditions

Logical operators characterized by relative homology groups

Potential improvements in quantum error correction

Abstract

A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups.