Design Automation in Quantum Error Correction

Abstract: Quantum error correction (QEC) underpins practical fault-tolerant quantum computing (FTQC) by addressing the fragility of quantum states and mitigating decoherence-induced errors. As quantum devices scale, integrating robust QEC protocols is imperative to suppress logical error rates below threshold and ensure reliable operation, though current frameworks suffer from substantial qubit overheads and hardware inefficiencies. Design automation in the QEC flow is thus critical, enabling automated synthesis, transpilation, layout, and verification of error-corrected circuits to reduce qubit footprints and push fault-tolerance margins. This chapter presents a comprehensive treatment of design automation in QEC, structured into four main sections. The first section delves into the theoretical aspects of QEC, covering logical versus physical qubit representations, stabilizer code construction, and error syndrome extraction mechanisms. In the second section, we outline the QEC design flow, detailing the areas highlighting the need for design automation. The third section surveys recent advancements in design automation techniques, including algorithmic $T$-gate optimization, modified surface code architecture to incorporate lesser qubit overhead, and machine-learning-based decoder automation. The final section examines near-term FTQC architectures, integrating automated QEC pipelines into scalable hardware platforms and discussing end-to-end verification methodologies. Each section is complemented by case studies of recent research works, illustrating practical implementations and performance trade-offs. Collectively, this chapter aims to equip readers with a holistic understanding of design automation in QEC system design in the fault-tolerant landscape of quantum computing.