Advantage in distributed quantum computing with slow interconnects

The main bottleneck for distributed quantum computing is the rate at which entanglement is produced between quantum processing units (QPUs). In this work, we prove that multiple QPUs connected through slow interconnects can outperform a monolithic architecture made with a single QPU. We consider a distributed quantum computing model with the following assumptions: (1) each QPU is linked to only two other QPUs, (2) each link produces only one Bell pair at a time, (3) the time to generate a Bell pair is τ_e times longer than the gate time. We propose a distributed version of the CliNR partial error correction scheme respecting these constraints and we show through circuit level simulations that, even if the entanglement generation time τ_e is up to five times longer than the gate time, distributed CliNR can achieve simultaneously a lower logical error rate and a shorter depth than both the direct implementation and the monolithic CliNR implementation of random Clifford circuits. In the asymptotic regime, we relax assumption (2) and we prove that links producing O\(t/ln t\) Bell pairs in parallel, where t is the number of QPUs, is sufficient to avoid stalling distributed CliNR, independently of the number of qubits per QPU. This demonstrates the potential of distributed CliNR for near-term multi-QPU devices. Moreover, we envision a distributed quantum superiority experiment based on the conjugated Clifford circuits of Bouland, Fitzsimons and Koh implemented with distributed CliNR.