We introduce qruise-toolset, a differentiable quantum simulation toolbox with a Python interface and a Julia simulation backend. The toolbox enables researchers and companies to build faithful digital twin models of their hardware for fast calibration and prototyping via closed-loop quantum optimal control strategies at the pulse level. Moreover, the realistic behaviour of the control stack and the pulse delivery via the signal chain is an indispensable part of the toolbox, allowing the user to explore the limitations of the control stack components.