Constant-Overhead Fault-Tolerant Bell-Pair Distillation using High-Rate Codes

We present a fault-tolerant Bell-pair distillation scheme achieving constant overhead through high-rate quantum low-density parity-check (qLDPC) codes. Our approach maintains a constant distillation rate equal to the code rate while requiring no additional overhead beyond the physical qubits of the code. Full circuit-level analysis demonstrates fault-tolerance for input Bell pair infidelities below a threshold $\sim 10\%$, readily achievable with near-term capabilities. Unlike previous proposals, our scheme keeps the output Bell pairs encoded in qLDPC codes at each node, eliminating un-encoding overhead and enabling direct use in distributed quantum applications through recent advances in qLDPC computation. These results establish qLDPC-based distillation as a practical route toward resource-efficient quantum networks and distributed quantum computing.