  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 $F$.
