Fault-Tolerant Logical Operations and Efficient State Preparation in Modular Quantum Architectures with Noisy Interfaces
Modular quantum computing is a leading paradigm for scaling quantum computation beyond the resource limitations of monolithic devices. In this architecture, multiple quantum processing units (QPUs), employing identical or distinct qubit modalities, are interconnected via shared entanglement. Here, we investigate how errors at module interfaces and within individual QPUs affect fault-tolerant computation when qubits are encoded using the rotated surface code. Going beyond the logical-memory benchmark, we perform circuit-level simulations of fault-tolerant nonlocal CNOT gates implemented via lattice surgery between QPUs connected by noisy Bell pairs, and analyze the resulting logical error rates. Our results show that interfaces can tolerate noise up to an order of magnitude higher than intra-QPU noise, with only a minor reduction in the fault-tolerance threshold. We further develop an efficient protocol for preparing distributed fault-tolerant logical GHZ states, reducing ancilla overhead, time, and nonlocal Bell-pair consumption. We show that ancilla minimization in this setting is equivalent to a vertex-cover problem on an associated graph, and introduce a polynomial-time heuristic algorithm for finding low-overhead solutions. Our results provide quantitative evidence that distributed quantum error correction can enable scalable, fault-tolerant quantum computation in modular architectures.