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

Abstract

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 on a consistent basis has remained elusive. Addressing this gap, this paper presents the first benchmarking framework for QECCs, introducing a set of universal parameters. By evaluating eight prominent QECCs, we propose a comprehensive suite of eight parameters for their analysis. Our methodology establishes a universal benchmarking approach and highlights the complexity of quantum error correction, indicating that the choice of a QECC depends on the unique requirements and limitations of each scenario. 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 novel 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.

12 pages, 14 figures, 2 tables

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