q-de Rham complexes of higher level

In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on higher-level q-crystalline site, which was introduced in the previous article of the author. One complex is the q-analog of the higher de Rham complex constructed by Miyatani, and another complex is the q-analog of the jet complex constructed by Le Stum-Quirós. The complexes we constructed can also be regarded as the higher-level analogs of the q-de Rham complex.