We report on the preparation of a large quantum register of 5612 qubits, with the unprecedented high global fidelity of (F\simeq 0.9956). This was achieved by applying an improved cooperative quantum information erasure (CQIE) protocol [Buffoni, L. and Campisi, M., Quantum 7, 961 (2023)] to a programmable network of superconducting qubits featuring a high connectivity. At variance with the standard method based on the individual reset of each qubit in parallel, here the quantum register is treated as a whole, thus avoiding the well-known orthogonality catastrophe wehereby even an extremely high individual reset fidelity (f) results in vanishing global fidelities (F=f^N) with growing number (N) of qubits.