Explain the theoretical underpinnings and implementation details of the Surface Code for quantum error correction. Discuss the topology of the qubit lattice required to implement a logical qubit with a specific distance (e.g., d=5). Describe the syndrome measurement cycle for detecting X and Z errors using ancillary qubits. Analyze the fault-tolerance threshold of the Surface Code and discuss the resource overhead (number of physical qubits required per logical qubit) required to achieve a logical error rate of 10^-15. Include a discussion on how logical gate operations (such as the CNOT gate) are performed transversally or via lattice surgery in this framework.