Snakes and Ladders: Adapting the surface code to defects

TL;DR

This paper introduces 'Snakes and Ladders', a suite of methods for adapting surface code quantum error correction to defective qubits, significantly improving logical performance in the presence of fabrication imperfections.

Contribution

The paper presents novel algorithms and heuristics for optimizing surface code patches with defects, enhancing fault tolerance in realistic quantum hardware.

Findings

Improved code distance in defective surface codes

Enhanced logical performance comparable to defect-free codes

Effective strategies for adapting to various defect configurations

Abstract

One of the critical challenges solid-state quantum processors face is the presence of fabrication imperfections and two-level systems, which render certain qubits and gates either inoperable or much noisier than tolerable by quantum error correction protocols. To address this challenge, we develop a suite of novel and highly performant methods for adapting surface code patches in the presence of defective qubits and gates, which we call \emph{Snakes and Ladders}. We explain how our algorithm generates and compares several strategies in order to find the optimal one for any given configuration of defective components, as well as introduce heuristics to improve runtime and minimize computing resources required by our algorithm. In addition to memory storage we also show how to apply our methods to lattice surgery protocols. Compared to prior works, our methods significantly improve the code distance of the adapted surface code patches for realistic defect rates, resulting in a logical performance similar to that of the defect-free patches.