Convergence rate of algorithms for solving linear equations by quantum annealing
V. S. Shalgin, Tikhomirov, S. · arXiv (Cornell University) · 2023
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.