Developing and Analyzing the Defect-Based Surface Codes Using Optimization Algorithms

Fault tolerance is crucial for enabling large-scale quantum computations, with surface codes emerging as prominent error correction techniques due to their high error threshold and reliance on nearest-neighbor interactions. Despite the advantages of surface codes, they demand a substantial number of qubits to encode a single logical qubit, making them resource-intensive. Two primary approaches exist to encode multiple logical qubits: patch-based and defect-based. This study focuses on the latter approach, which involves creating holes in the surface code for logical qubit encoding. With the defect-based approach, we need to account for trade-offs between the number of logical qubits and the logical error rates, so we employ an optimization algorithm to evaluate the maximum number of logical qubits for a given error rate. Through a series of experiments, we assess the limitations of the defect-based approach and investigate the impact of various hole types on logical qubit encoding.