As a key enabler for sixth-generation (6G) wireless communications, reconfigurable intelligent surfaces (RISs) provide the flexibility to control signal strength. Nevertheless, optimizing hundreds of elements is computationally expensive. To overcome this challenge, we present a quantum framework (QGCN) to jointly optimize the physical and electromagnetic response of a double-sided RIS design that incorporates discrete phase shifts and inter-element coupling. The core contribution is the adaptive activation or deactivation of elements, allowing a virtual spacing mechanism using PIN diode switches. We then solve a multi-objective problem that maximizes the minimum user data rate subject to constraints on aperture length and mutual coupling between active elements. Experimental results on IBM Quantum's 127-qubit ibm_kyiv superconducting processor demonstrate that the proposed QGCN algorithm reduces both per-iteration computational complexity and memory requirements compared to existing approaches. Also, the QGCN outperforms classical graph neural networks (GNN) on an equivalent graph topology by an additional +0.38 bps/Hz. This advantage is increasing with increasing array sizes.