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