A Cross-Platform Analysis of High-Performance Quantum Error Correction Codes

Abstract

The theory of quantum error correction was established decades ago. Yet the limitation of the quantum computing platforms in terms of noise level and available physical qubit count persists, which greatly hinders the development of scalable quantum computing systems. In this paper, we present analytical estimates of logical error rates of advanced QEC codes across leading hardware platforms and distributed quantum computing systems using a simple but unified framework. The analysis captures two dominant contributors to logical error: code structure and two-qubit gate overhead. The framework provides a fast estimate of logical error rates and identification of dominating factors in different hardware platforms, such as circuit volume, routing overhead, inter-QPU operations, or asymmetric noise protection. We show that several qualitative trends observed in larger-scale simulations can be reproduced and interpreted analytically within this framework. We further demonstrate that the framework can be used to find the sweet spot design region of distributed QEC, which is critical for the design of distributed quantum computing systems.