Quantum Error Correction with the Semion Code

TL;DR

This paper introduces the semion code, a novel topological quantum error correcting code that extends the double semion model, featuring open and closed string operators for error recovery and logical operations, and fitting into the stabilizer formalism.

Contribution

The paper develops a full quantum error correction procedure with the semion code, a non-CSS topological code that is stabilizer-compatible and provides detailed microscopic descriptions of semion creation.

Findings

Constructed open string operators for error recovery

Designed closed string operators for logical operations

The code is non-CSS and fits into the stabilizer formalism

Abstract

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string operators that implement the basic logical operations for information processing. Physically, the new open string operators provide a detailed microscopic description of the creation of semions at their endpoints. Remarkably, topological properties of the string operators are determined using fundamental properties of the Hamiltonian, namely the fact that it is composed of commuting local terms squaring to the identity. In all, the semion code is a topological code that, unlike previously studied topological codes, it is of non-CSS type and fits into the stabilizer formalism. This is in sharp contrast with previous attempts yielding non-commutative codes.