Numerical methods for the simulation of quantum walks and quantum annealing

Abstract

It is known that Chebyshev based polynomial approximation gives a near-optimal rate of convergence for calculating a function of a Hermitian matrix. However, previous work has not discussed the option of true minimax approximation, nor the specifics of writing a high performance implementation with a rigorous analysis of errors. This work provides such an analysis and an open-source implementation of three approximation methods in C++.

15 pages, 6 figures. This paper covers the numerical details of https://arxiv.org/abs/2511.01312