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 e6f462f3840780bbb511d3cab3fe651270de0dee 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 (Symmetrizised quantum variant of Chebyshev Iteration), or qsvt (QSVT solver from https://doi.org/10.1145/3313276.3316366, 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