Linnea Grans-Samuelsson

Distributed architectures have been proposed as a pathway to large-scale quantum computers. Combined with the need for fault-tolerance, such architectures require distributed quantum error correction, where an important primitive is distributed stabilizer measurement. This primitive appears not only in the context of distributed quantum memories, but is also required for lattice surgery between logical qubits hosted on separate QPUs. We consider a setting where multiple QPUs are connected through long-range interconnects using shared Bell pairs, and where the interconnects are assumed to be significantly noisier than on-chip operations. We extend the work in arXiv:2506.17181 on fault tolerance by construction to this setting, and apply it to derive distributed stabilizer measurements that are robust to the additional noise on the interconnects. We recover conventional entanglement distillation, but also find more dynamical protocols that allow for space-time trade-offs. Through such trade-offs, the circuits can be adapted to resource constraints, e.g. on the Bell pair generation rate or the space available for on-chip auxiliary qubits. Noting that full local fault-tolerance is not always needed to preserve the correct scaling of logical error rates, we further optimize the circuits depending on the surrounding context. We consider in particular the surface code and the color code, both as distributed memories and in the case of lattice surgery across separate QPUs. Here, robustness to certain hook and readout errors reduces the number of Bell pairs required. We numerically benchmark the resulting implementations at an interconnect noise rate scaling as the cube root of p compared to an on-chip noise rate p.