Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements

TL;DR

This paper introduces a method to adapt Floquet codes for hardware with defective qubits, maintaining fault tolerance without extra connectivity or code modifications, and demonstrates its effectiveness through numerical simulations.

Contribution

A novel approach to accommodate defective qubits in Floquet codes without additional hardware requirements or code modifications, enhancing their practicality on real quantum devices.

Findings

Fault-tolerant up to 12% defect probability in planar honeycomb code

Performance comparable to surface code despite sparser connectivity

Method adaptable to various hardware configurations

Abstract

Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has been how to run Floquet codes on devices which have defective -- and therefore unusable -- qubits. This is an under-studied issue of crucial importance for running such codes on realistic hardware. To address this challenge, we introduce a new method of accommodating defective qubits on a wide range of two-dimensional Floquet codes, which requires no additional connectivity in the underlying quantum hardware, no modifications to the original Floquet code's measurement schedule, can accommodate boundaries, and is optimal in terms of the number of qubits and stabilisers removed. We numerically demonstrate that, using this method, the planar honeycomb code is fault tolerant up to a fabrication defect probability of $\approx 12\%$. We find the fault-tolerant performance of this code under defect noise is competitive with that of the surface code, despite its sparser connectivity. We finally propose multiple ways this approach can be adapted to the underlying hardware, through utilising any additional connectivity available, and treating defective auxiliary qubits separately to defective data qubits. Our work therefore serves as a guide for the implementation of Floquet codes in realistic quantum hardware.