Constrained Optimal Polynomials for Quantum Linear System Solvers – Numerical Data

The data was generated using the code at https://github.com/MDeiml/quantum-krylov and is consistent with the commit 47fbd31c425aeb45d058a62729cb4b3fe6559527 and the files main_cap.py and main_semi_iterative.py therein. The meaning of the columns in the csv files is as follows: steps: Step n of the solver samples: Number of samples used for each measurement transform: Transform, None, square, or square_outer, applied to the solver polynomial adaptive (cap_...csv only): Wether the CAP (True) or CUP (False) solver was used poly_kind (semi_iterative...csv only): Kind of semi iterative solver, one of cheb (Chebyshev Iteration), q_cheb [GKS24], chebopt [SNW+25], or qsvt [GSLW19, Theorem 41] noise: Expected number of Pauli flips per application of the block encoding kappa: Upper bound of the condition number of the linear system, which is passed to the solver num_clusters: Number of eigenvalue clusters, or None for uniform eigenvalues complexity: Number of times the block encoding of the matrix was used on average error <x> percentile: x-th percentile of the relative error [GKS24] S. Gribling, I. Kerenidis, and D. Szilágyi. “An Optimal Linear-combination-of-unitaries-based Quantum Linear System Solver”. ACM Trans. Quantum Comput. 5, 1–23 (2024). https://dx.doi.org/10.1145/3649320[SNW+25] C. Sünderhauf, Z. Németh, A. Walayat, A. Patterson, and B. K. Berntson. “Matrix inversion polynomials for the quantum singular value transformation” (2025). http://arxiv.org/abs/2507.15537[GSLW19] A. Gilyén, Y. Su, G. H. Low, and N. Wiebe. “Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics”. In Proc. 51st Annu. ACM SIGACT Symp. Theory Comput. Pages 193–204. (2019). https://dx.doi.org/10.1145/3313276.3316366本数据集依托代码仓库 https://github.com/MDeiml/quantum-krylov 处的代码生成，与该仓库的提交版本 commit 47fbd31c425aeb45d058a62729cb4b3fe6559527，以及其中的 main_cap.py 和 main_semi_iterative.py 文件保持一致。 CSV 文件各列的含义如下： steps：求解器的第 n 步 samples：单次测量所使用的样本数量 transform：应用于求解器多项式的变换，可选值为 None、square 或 square_outer adaptive（仅 cap_*.csv 文件适用）：标识所用求解器类型，取值为 True 时使用 CAP 求解器，False 时使用 CUP 求解器 poly_kind（仅 semi_iterative_*.csv 文件适用）：半迭代求解器的类型，可选值包括 cheb（切比雪夫迭代）、q_cheb [GKS24]、chebopt [SNW+25]、qsvt [GSLW19, 定理 41] noise：单次矩阵块编码（block encoding）操作的预期泡利翻转（Pauli flips）数量 kappa：线性系统条件数的上界，该参数将被传入求解器 num_clusters：特征值簇的数量，若特征值为均匀分布则取值为 None complexity：平均情况下矩阵块编码的调用次数 error <x> percentile：相对误差的 x 百分位数 参考文献： [GKS24] S. Gribling、I. Kerenidis 与 D. Szilágyi. 《基于最优线性幺正组合的量子线性系统求解器》. ACM Transactions on Quantum Computing，第5卷，1-23页（2024）. https://dx.doi.org/10.1145/3649320 [SNW+25] C. Sünderhauf、Z. Németh、A. Walayat、A. Patterson 与 B. K. Berntson. 《面向量子奇异值变换（quantum singular value transformation）的矩阵逆多项式》（2025）. http://arxiv.org/abs/2507.15537 [GSLW19] A. Gilyén、Y. Su、G. H. Low 与 N. Wiebe. 《量子奇异值变换及拓展：量子矩阵算术的指数级改进》. 收录于第51届ACM SIGACT年度计算理论研讨会论文集，193-204页（2019）. https://dx.doi.org/10.1145/3313276.3316366