@NathanReading I edited this question again and explain the motivation

@SamHopkins, thanks for your comment, it's a typo, it's $\mathbb{C}^k$

@R. van Dobben de Bruyn, Then then question is : can we build two chain complex of $k[x]$-module and a map $f$ between them, that $f$ induce quasi-isomorphism on associated graded pieces of $(x)$-adic filtration and $f$ itself is not a homotopy equivalence. May be this kind of example is easy?

@R. van Dobben de Bruyn, thank you for your comment, I think there are also a small gap in your counterexample. I believe it is easy to give two chain of $k[x]$-module that is quasi-isomorphic but not homotopy equivalence, but if we want it to be a counterexample of my question, the associated graded pieces of (x)-adic filtration should be quasi-isomorphic.