Method, apparatus and product for modeling of quantum circuits and usages thereof. A method comprises obtaining a model of a quantum circuit that comprises a set of decision variables, corresponding domains, and constraints, wherein the set of decision variables comprise gate assignment decision variables that define an assignment of a gate to a qubit in a cycle in the quantum circuit. The method comprises automatically determining a set of valuations for the set of decision variables. The set of valuations are selected from the corresponding domains and satisfy the constraints. Based on the set of valuations the quantum circuit is synthesized.