Inverse-coefficient black-box quantum state preparation

Abstract

Black-box quantum state preparation is a fundamental building block for many higher-level quantum algorithms. The basic task of black-box state preparation is to transduce the data encoded as computational basis of quantum state into the amplitude. In the present work, we address the problem of transducing the reciprocal of the data, not the data itself into the amplitude, which is called the inverse-coefficient problem. This algorithm can be used directly as a subroutine in the matrix inversion algorithms. Furthermore, we extend this approach to address the more general nonlinear-coefficient problem in black-box state preparation. Our algorithm is based on the technique of inequality test. It can greatly relieve the need to do quantum arithmetic and the error is only resulted from the truncated error of binary string. The present algorithms enrich the algorithm library of black-box quantum state preparation and will be useful ingredients of quantum algorithm to implement non-linear quantum state transformations.