  In maximally supersymmetric four-dimensional gauge theories planar on-shell
diagrams are closely related to the positive Grassmannian and the cell
decomposition of it into the union of so called positroid cells \cite{A}. We
establish that volume forms on positroids used to express scattering amplitudes
can be $q$-deformed to Hochschild homology classes of corresponding quantum
algebras. The planar amplitudes are represented in \cite {A} as sums of
contributions of some set of positroid cells; we quantize these contributions.
In classical limit our considerations allow us to obtain explicit formulas for
contributions of positroid cells to scattering amplitudes.
