We consider various iterative algorithms for solving the linear equation ax=b using a quantum computer operating on the principle of quantum annealing. Assuming that the computer's output is described by the Boltzmann distribution, it is shown under which conditions the equation-solving algorithms converge, and an estimate of their convergence rate is provided. The application of this approach to algorithms using both an infinite number of qubits and a small number of qubits is discussed.
@article{arxiv.2310.15441,
title = {Convergence rate of algorithms for solving linear equations by quantum annealing},
author = {V. Shalgin and S. Tikhomirov},
journal= {arXiv preprint arXiv:2310.15441},
year = {2023}
}