Limited Connectivity Quantum Architectures: Enhancing Surface Code Implementation Through Routing Qubits

In quantum computer architectures, low connectivity poses a major challenge in implementing efficient error correction codes such as surface codes that require high connectivity degrade when direct interaction between qubits is limited, making accurate error correction and reliable computation difficult. To implement surface codes with distances of 2 and 3 in quantum computer structures with limited connectivity, we analyze resources by the number of qubits and by the number of CNOT gates, suggesting a way to expand connectivity using routing qubits and SWAP gates.