Cache Hierarchy and Vectorization Analysis of Lindblad Master Equation Simulation for Near-Term Quantum Control

Quantum Physics [Submitted on 17 Mar 2026] Cache Hierarchy and Vectorization Analysis of Lindblad Master Equation Simulation for Near-Term Quantum Control Rylan Malarchick Simulation of open quantum systems via the Lindblad master equation is a computational bottleneck in near-term quantum control workflows, including optimal pulse engineering (GRAPE), trajectory-based robustness analysis, and feedback controller design. For the system sizes relevant to near-term quantum control (d = 3 for a single transmon with leakage, d = 9 for two-qubit, and d = 27 for three-qubit), the dominant cost per timestep is a (d^2 \times d^2) complex matrix-vector multiplication: a 9\times9, 81\times81, or 729\times729 dense matvec, respectively. The working set sizes (1.5 KB, 105 KB, and 8.1 MB) straddle the L1, L2, and L3 cache boundaries of modern CPUs, making this an ideal system for cache-hierarchy performance analysis. We characterize the arithmetic intensity (\approx 1/2 FLOP/byte in the large-d limit), construct a Roofline model for the propagation kernel, and systematically vary compiler flags and data layout to isolate the contributions of auto-vectorization, fused multiply-add, and structure-of-arrays (SoA) memory layout. We show that SoA layout combined with -O3 -march=native -ffast-math yields 2--4\times speedup over scalar array-of-structures baselines, and that -ffast-math is essential for enabling GCC auto-vectorization of complex arithmetic. These results motivate a set of concrete recommendations for authors of quantum simulation libraries targeting near-term system sizes. Comments: 6 pages, 2 figures, 4 tables, 2 listings Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18052 [quant-ph]   (or arXiv:2603.18052v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.18052 Focus to learn more Submission history From: Rylan Malarchick [view email] [v1] Tue, 17 Mar 2026 21:53:31 UTC (53 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)