A Genus-two Surface Code

TL;DR

This paper introduces a novel genus-two surface code based on a rhombus-tiled planar tessellation, enabling efficient encoding of multiple logical qubits with enhanced error correction and robustness against noise.

Contribution

It presents a new double-toric surface code design that improves logical qubit encoding and error correction capabilities using a specific tessellation pattern.

Findings

Able to encode at least n/3 logical qubits with n data qubits

Achieves larger code distances for better error correction

Demonstrates robustness of logical qubits under external noise

Abstract

We construct a double-toric surface code by exploiting the planar tessellation using a rhombus-shaped tile. With n data qubits, we are able to encode at least n/3 logical qubits or quantum memories. By a suitable arrangement of the tiles, the code achieves larger distances, leading to significant error-correcting capability. We demonstrate the robustness of the logical qubits thus obtained in the presence of external noise. We believe that the optimality of the code presented here will pave the way for design of efficient scalable architectures.