Accelerating the Tesseract Decoder for Quantum Error Correction

TL;DR

The paper tackles decoding speed bottlenecks in quantum error correction by accelerating the Tesseract A*–based decoder. Through profiling, it applies four hardware-aware optimizations—data-layout reorganization, replacing bit-packed structures, precomputed cost lower bounds for early exits, and hardware-accelerated hashing using boost::dynamic_bitset—targeting the get_detcost bottleneck. Across Color Codes, Surface Codes, Bivariate-Bicycle Codes, and Transversal CNOT Protocols, the approach yields average speedups near $2\times$, frequently exceeding $2.5\times$, with a peak above $5\times$ on demanding Bivariate-Bicycle configurations. Results are validated across three CPU architectures and multiple noise models, underscoring robust portability and establishing a practical benchmark for high-performance QEC software.

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.

Figures (6)

• Figure 1: Comparison of memory access patterns between std::vector<bool> and std::vector<char>. While std::vector<bool> minimizes memory footprint through bit-packing, frequent access requires proxy objects to perform bit-wise shifting and masking, inducing significant computational overhead compared to direct byte-addressable access in std::vector<char>.
• Figure 2: Data reorganization and early-exit logic within the get_detcost function. Consolidating frequently accessed elements from separate vectors into a single contiguous structure (Array of Structs) optimizes CPU cache performance. The integrated early-exit strategy utilizes pre-calculated error cost lower bounds to bypass unnecessary computations.
• Figure 3: Decoding speedups across various code families and configurations for experiments on the first architecture using the short beam configuration: (a) Color Codes at $p=0.001$; (b) Color Codes at $p=0.002$; (c) Bivariate-Bicycle Codes at $p=0.001$; (d) Bivariate-Bicycle Codes at $p=0.002$; (e) Surface Codes; (f) Transversal CNOT Protocols for Surface Codes.
• Figure 4: Decoding speedups achieved across various code families and configurations for the second (Cascade Lake) and third (Sapphire Rapids) architectures, utilizing the long beam configuration: (a) Color Codes at $p=0.001$; (b) Color Codes at $p=0.002$; (c) Bivariate-Bicycle Codes at $p=0.001$; (d) Bivariate-Bicycle Codes at $p=0.002$; (e) Surface Codes; (f) Transversal CNOT Protocols for Surface Codes.
• Figure 5: Cache miss rate reduction within the get_detcost kernel for long beam experiments on the Cascade Lake architecture: (a) Color Codes at $p=0.001$; (b) Color Codes at $p=0.002$; (c) Bivariate-Bicycle Codes at $p=0.001$; (d) Bivariate-Bicycle Codes at $p=0.002$; (e) Surface Codes; (f) Transversal CNOT Protocols for Surface Codes.