Accelerating the Tesseract Decoder for Quantum Error Correction

Abstract: Quantum Error Correction (QEC) is essential for building robust, fault-tolerant quantum computers; however, the decoding process often presents a significant computational bottleneck. Tesseract is a novel Most-Likely-Error (MLE) decoder for QEC that employs the A* search algorithm to explore an exponentially large graph of error hypotheses, achieving high decoding speed and accuracy. This paper presents a systematic approach to optimizing the Tesseract decoder through low-level performance enhancements. Based on extensive profiling, we implemented four targeted optimization strategies, including the replacement of inefficient data structures, reorganization of memory layouts to improve cache hit rates, and the use of hardware-accelerated bit-wise operations. We achieved significant decoding speedups across a wide range of code families and configurations, including Color Codes, Bivariate-Bicycle Codes, Surface Codes, and Transversal CNOT Protocols. Our results demonstrate consistent speedups of approximately 2x for most code families, often exceeding 2.5x. Notably, we achieved a peak performance gain of over 5x for the most computationally demanding configurations of Bivariate-Bicycle Codes. These improvements make the Tesseract decoder more efficient and scalable, serving as a practical case study that highlights the importance of high-performance software engineering in QEC and providing a strong foundation for future research.