Quantum error correction beyond the toric code: dynamical systems meet encoding

TL;DR

This paper introduces new high-genus surface codes inspired by classical billiard topologies, achieving improved encoding rates, code distance, and noise immunity in quantum error correction.

Contribution

It constructs novel surface codes of higher genus based on classical billiard topologies, extending quantum error correction beyond the toric code.

Findings

Improved encoding rates and code distances.

Enhanced immunity against noise.

Construction of surface codes of genus two and five.

Abstract

We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards. Corresponding to the fundamental domains of rhombus and square torus billiard, surface codes of genus two and five are presented here. There is significant improvement in encoding rates and code distance, in addition to immunity against noise.