Quantum power iteration to efficiently obtain the dominant eigenvector from diagonalizable nonnegative matrices

This manuscript presents a quantum computing implementation of power iteration for diagonalizable nonnegative matrices that offers a significant speed increase for large matrices, achieving \(O(K\hbox {max}(m_i)+N)\) $O(K\text{max}(m_i)+N)$ time complexity for each iteration. The computational approach presented in this manuscript may be directly applied to numerous other algorithms derived from power iteration, ultimately allowing near-term quantum devices to facilitate a broad range of analyses that would otherwise be infeasible.