Robust hybrid qubit plane architecture for enhancing lattice-surgery-based surface codes

Quantum computing offers unprecedented speed and power for solving complex problems, but its susceptibility to errors makes error-correction codes crucial. An important metric for evaluating the performance of error-correction codes is the code distance, which measures the number of errors a code can correct. Current qubit-plane architectures are implemented using the same code distance. However, a larger code distance reduces the logical error rate but increases resources. In fact, distance-5 code uses more resources but offers higher resilience to logical errors compared to distance-3 code. We propose a qubit-plane architecture for rotated and unrotated surface codes called Qentaurus that combines various code distances of logical qubits for robust error correction while maintaining qubit efficiency. Qentaurus is designed to be highly scalable regarding computation, layout, and code distance. We performed a case study using Qentaurus with distance-3 and -7 codes to evaluate the performance. Moreover, we additionally developed a qubit placement scheme that considers the critical path of the quantum circuit to reduce the logical error rate and gate count. Our main experimental results demonstrated that Qentaurus considerably reduces the overall logical error rate (by 15.76% on average and up to 25.25%) than that of the Distance-3 Checkerboard architecture. After additionally implementing the qubit placement scheme, the average reduction increases to 13.44% (up to 39.07%). Notably, the Qentaurus-3&7 maintains logical error rates comparable to those of the Distance-5 Checkerboard, achieving considerable qubit efficiency. The Distance-5 Checkerboard demands 227.7% more physical qubits than that required by the Distance-3 Checkerboard, while Qentaurus-3&7 utilizes just 131.2% of the physical qubits required by Distance-3 the Checkerboard, marking a substantial reduction of 96.5% in the resource gap. The overall gate count is reduced by an average of 1.74% with Qentaurus alone and by 3.33% on average with the qubit placement scheme. We believe that the proposed Qentaurus and qubit placement scheme have the potential to significantly improve the error-correction performance of large-scale quantum computers in practical applications.