Accelerating the Tesseract Decoder for Quantum Error Correction

TL;DR

This paper enhances the Tesseract decoder for quantum error correction by applying low-level optimizations, resulting in 2x to 5x speedups across various code families, thus improving scalability and practical applicability.

Contribution

The paper introduces systematic low-level performance optimizations to the Tesseract decoder, significantly increasing its speed and efficiency for quantum error correction tasks.

Findings

Achieved approximately 2x speedup for most code families.

Exceeded 2.5x speedup in several configurations.

Peak performance gain of over 5x for complex Bivariate-Bicycle Codes.

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.