Abstract: Although extended gate sets exhibit significant advantages in compiling noisy intermediate-scale quantum circuits on superconducting qubits, their potential applications in quantum error correction still need further exploration. In this paper, we comprehensively analyze two recent proposals, Halma scheme and Louvre scheme, both of which leverage extended gate sets to reduce the hardware overhead of fault-tolerant quantum computing. The Halma scheme demonstrates how the surface codes can be implemented on a lattice with defects, with lower overhead compared to prior approaches. In addition, the scheme has good compatibility with the previous superstabilizer scheme, enabling fallback to the superstabilizer scheme in case of defect clustering and thereby supporting hybrid usage. The Louvre scheme reduces the qubit connectivity requirements of generalized bicycle codes. In both schemes, the extended gate sets facilitate flexible qubit routing, thereby allowing for the reuse of qubits and interconnects. These approaches have demonstrated how extended gate sets can pave a path toward practical fault-tolerant quantum computing on superconducting platforms.

Key words: quantum computing, quantum information and processing, quantum error correction code, quantum gate set, surface code, generalized bicycle code