Error Suppression in Distributed Quantum Computing with Heterogeneous-Distance Lattice Surgery

Distributed quantum computing requires connecting multiple quantum processing units (QPUs) to scale fault-tolerant operations. However, inter-QPU links are typically much noisier than local gates. The authors investigate whether it is possible to maintain high-fidelity logical operations across these noisy boundaries without uniformly increasing the code distance of all data patches, which would otherwise impose a prohibitive physical-qubit overhead.

The researchers propose a heterogeneous-distance lattice surgery protocol using an eight-data-patch ancilla-mediated (8-DAM) architecture. In this design, the central ancilla patch spanning the inter-QPU boundary is enlarged (e.g., to distance 2d+1), while the data patches retain their original distance d. To maintain fault tolerance and prevent hook errors—correlated errors that propagate during syndrome extraction—the protocol employs a traveling stabilizer scheduling technique. The authors evaluate this construction through circuit-level simulations of rotated surface codes, comparing the logical readout error rates of their heterogeneous layouts against uniform-distance baselines under varying link-noise levels.

The 8-DAM architecture effectively concentrates protection at the noisy interface. Simulations show that logical readout error rates in the 8-DAM construction depend only weakly on link noise, providing a significant advantage over uniform-distance implementations as link error rates increase. For instance, a 5-11-5 heterogeneous construction achieves logical error suppression comparable to a uniform distance-9 code while requiring approximately 28% fewer physical qubits. Furthermore, the authors demonstrate that the 8-DAM layout can support two simultaneous distributed logical CNOT operations using a single enlarged ancilla, yielding lower logical error rates and greater stability than two independent distributed CNOTs.