Distributed Variational Quantum Optimisation by Entanglement-Selective Transport

Abstract: Distributed quantum optimisation is challenging because computing the problem cost function across multiple quantum processors requires non-local gates, which can incur overhead in latency and fidelity. Here we introduce QESTO, a distributed variational ansatz for graph-based discrete optimisation that requires only persistent pre-shared Bell pairs for remote operations. Using local operations, it encodes local constraint information in the Bell pairs that is leveraged to produce amplitude transfer towards globally valid distributed solution states. QESTO requires one Bell pair per distributed edge of the problem graph and, after initialisation of the Bell states, uses no non-local gates. On two bounded weighted Wang tile-matching problem ensembles, QESTO achieves stronger convergence to low-cost tilings than equivalently partitioned QAOA with no distributed gates at ansatz depths of two or higher, and exceeds the mean performance of monolithic QAOA at the deepest studied depth in both ensembles. These results suggest that persistent entanglement can support useful variational communication while reducing per-layer non-local gate overhead.