Quantum linear system algorithm applied to communication systems

A quantum linear system algorithm (QLSA) can solve linear equations more efficiently than classical ones. However, we cannot know the value of each component of a solution directly because a QLSA produces a solution as a quantum state. In this paper, we present a method to obtain classical information of a solution with the exponential quantum advantage of a QLSA when the values of a solution are on a rectangular grid in the complex plane. Our method can extract both the amplitude and phase information by modifying the given matrix. Moreover, we show an application to a specific problem in communication systems.