Trident: Efficient Load Verification for Yoked Surface Codes using a Three-Level Memory Hierarchy

arXiv:2610.32152v1 Announce Type: new Abstract: Fault-Tolerant Quantum Computers (FTQCs) commonly use the surface code to encode program qubits as error-corrected logical qubits. Unfortunately, the surface code has a poor encoding rate, so recent work has proposed Yoked Surface Codes (YSCs), which concatenate the surface code with a high-rate quantum code. The surface code qubits in YSCs are protected by the checks, or yokes, of the high-rate code. YSCs have 1D and 2D variants, which are $1.8\times$ and $4.5\times$ more efficient than the surface code, respectively. Modern FTQC architectures use a two-level hierarchy: surface codes perform logical operations (compute) while 2D YSCs store idle program qubits (memory).