Magic Mirror on the Wall, How to Benchmark Quantum Error Correction Codes, Overall?

Quantum Error Correction Codes (QECCs) are pivotal in advancing quantum computing by protecting quantum states against the adverse effects of noise and errors. With a variety of QECCs developed, including new developments and modifications of existing ones, selecting an appropriate QECC tailored to specific conditions is crucial. Despite significant improvements in the field of QECCs, a unified methodology for evaluating them consistently has remained elusive. This paper addresses this gap by introducing a set of eight universal parameters and evaluating nine prominent QECCs for these parameters. We establish a universal benchmarking approach and highlight the complexity of quantum error correction, indicating that the choice of a QECC depends on each scenario's unique requirements and limitations. Furthermore, we develop a systematic strategy for selecting QECCs that adapts to the specific requirements of a given scenario, facilitating a tailored approach to quantum error correction. Additionally, we introduce a QECC recommendation tool that assesses the characteristics of a given scenario provided by the user, subsequently recommending a spectrum of QECCs from most to least suitable, along with the maximum achievable distance for each code. This tool is designed to be adaptable, allowing for the inclusion of new QECCs and the modification of their parameters with minimal effort, ensuring its relevance in the evolving landscape of quantum computing.