This is an extended abstract of a lecture on some results obtained in collaboration with D. Rottensteiner and M. Ruzhansky, which can be found in [3], about the existence of a Weyl calculus on any graded Lie group. Below we will introduce a family of quantizations, the so called \(\tau \) -quantizations, and present the asymptotic formulas representing the building blocks of the corresponding pseudo-differential symbolic calculus. Then, we will say which one among the \(\tau \) -quantizations is a Weyl quantization on any graded group. Finally, we will show that the Weyl quantization is uniquely determined in the case of the Heisenberg group \(\mathbb {H}_n\) .