An Investigation of Functional Size Measurement of Error Correction Overhead in Quantum Software

Abstract

As quantum computing has progressed toward fault-tolerant implementations, quantum error correction (QEC) for quantum hardware and software has become a dominant concern. While conventional QEC measurements, such as qubit overhead, code distance, and error thresholds, quantify physical resource costs, they do not capture the software-level functionality introduced by error detection, correction, and fault-tolerant gate protocols. This study investigated the QEC contribution to the functional size of quantum software and demonstrated that this contribution can be systematically measured using the COSMIC Functional Size Measurement method. A gate-level sizing approach, known as Gates’ Occurrences, was used to quantify functional user requirements (FUR) associated with QEC processes, including logical encoding, syndrome extraction, and recovery operations. A prototype measurement tool, implemented in Qiskit (Version 0.7.2), enables the automated calculation of COSMIC Function Points (CFP) from annotated circuit representations. Case studies involving Bell state preparation, Grover’s search algorithm, and 15-to-1 magic state distillation revealed that QEC-related functionality can account for 70–85% of the total functional size, even under simplified encoding assumptions. The results underscore the importance of QEC for the functional size of quantum software. These findings offer a reproducible foundation for functional sizing and future fault-tolerant quantum applications.