Black-Box Quantum State Preparation with Inverse Coefficients

TL;DR

This paper introduces a new quantum algorithm for black-box state preparation with inverse coefficients, significantly reducing computational cost and extending to non-linear functions, with broad applicability in quantum algorithms.

Contribution

The paper presents a novel algorithm for black-box quantum state preparation with inverse coefficients, utilizing inequality test, and extends it to handle general non-linear functions.

Findings

Algorithm achieves low-cost state preparation with inverse coefficients.

Extension to non-linear coefficient functions broadens applicability.

Error is primarily due to binary string truncation.

Abstract

Black-box quantum state preparation is a fundamental building block for many higher-level quantum algorithms, which is applied to transduce the data from computational basis into amplitude. Here we present a new algorithm for performing black-box state preparation with inverse coefficients based on the technique of inequality test. This algorithm can be used as a subroutine to perform the controlled rotation stage of the Harrow-Hassidim-Lloyd (HHL) algorithm and the associated matrix inversion algorithms with exceedingly low cost. Furthermore, we extend this approach to address the general black-box state preparation problem where the transduced coefficient is a general non-linear function. The present algorithm greatly relieves the need to do arithmetic and the error is only resulted from the truncated error of binary string. It is expected that our algorithm will find wide usage both in the NISQ and fault-tolerant quantum algorithms.