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.

翻译：我们考虑利用基于量子退火原理的量子计算机求解线性方程$ax=b$的各种迭代算法。假设计算机的输出由玻尔兹曼分布描述，本文展示了在何种条件下这些方程求解算法能够收敛，并给出了其收敛速度的估计。进一步讨论了该方法在涉及无限量子比特数及少量量子比特数算法中的应用。