A Note on "Quantum Algorithm for Linear Systems of Equations"

TL;DR

This paper provides a simplified proof of the error and complexity analysis of the HHL quantum algorithm for linear systems, aiming to facilitate the development of new algorithms for computing functions of matrices.

Contribution

It offers a concise proof of the HHL algorithm's analysis, potentially enabling the creation of generalized algorithms for various matrix functions.

Findings

Simplified proof of HHL algorithm's error and complexity analysis

Potential for developing new quantum algorithms for matrix functions

Enhanced understanding of HHL's applicability to different tasks

Abstract

Recently, an efficient quantum algorithm for linear systems of equations introduced by Harrow, Hassidim, and Lloyd, has received great concern from the academic community. However, the error and complexity analysis for this algorithm seems so complicated that it may not be applicable to other filter functions for other tasks. In this note, a concise proof is proposed. We hope that it may inspire some novel HHL-based algorithms that can compute $F(A)|b\rangle$ for any computable $F$.