Bipartitioning of graph states for distributed Measurement-Based Quantum Computing

Measurement-Based Quantum Computing (MBQC) is inherently well-suited for Distributed Quantum Computing (DQC): once a resource state is prepared and distributed across a network of quantum nodes, computation proceeds through local measurements coordinated by classical communication. However, since non-local gates acting on different Quantum Processing Units (QPUs) are a bottleneck, it is crucial to optimize the qubit assignment to minimize inter-node entanglement of the shared resource. For graph state resources shared across two QPUs, this task reduces to finding balanced bipartitions with minimal cut rank. We introduce a simulated annealing-based algorithm that efficiently updates the cut rank when two vertices swap sides across a bipartition, such that computing the new cut rank from scratch, which would be much more expensive, is not necessary. Testing our approach on grid graphs, random graphs and measurement-based Quantum Approximate Optimization Algorithm (QAOA) instances, we find that it matches the quality of established hypergraph partitioning with the potential advantage of remaining invariant under local Clifford operations and thus independent of the chosen representative of the graph state.