Superconducting electro-mechanics to test Diósi-Penrose effects of general relativity in massive superpositions

Attempting to reconcile general relativity with quantum mechanics is one of the great undertakings of contemporary physics. Here, the authors present how the incompatibility between the two theories arises in the simple thought experiment of preparing a heavy object in a quantum superposition. Following Penrose's analysis of the problem, the authors determine the requirements on physical parameters to perform experiments where both theories potentially interplay. The authors use these requirements to compare different systems, focusing on mechanical oscillators that can be coupled to superconducting circuits.