Noise Thresholds for the [[4, 2, 2]]-concatenated Toric Code

TL;DR

This paper investigates a concatenated 2D topological code combining the [[4, 2, 2]] code with the toric code, revealing a noise threshold of approximately 0.41%, which surpasses known 2D color codes and has potential hardware applications.

Contribution

It introduces a new concatenated topological code with a higher noise threshold than existing 2D color codes, expanding possibilities for quantum hardware design.

Findings

Achieves a circuit-based noise threshold of ~0.41%.

Higher threshold than known 2D color codes.

Potential for hardware with both long-range and short-range gates.

Abstract

We analyze the properties of a 2D topological code derived by concatenating the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing check operators from the 2D square-octagon or 4.8.8 color code. We show that the resulting code has a circuit-based noise threshold of $\sim 0.41\%$ (compared to $\sim 0.6\%$ for the toric code in a similar scenario), which is higher than any known 2D color code. We believe that the construction may be of interest for hardware in which one wants to use both long-range two-qubit gates as well as short-range gates between small clusters of qubits.