Evolving a Multi-Population Evolutionary-QAOA on Distributed QPUs

Abstract: Our research combines an Evolutionary Algorithm (EA) with a Quantum Approximate Optimization Algorithm (QAOA) to update the ansatz parameters, in place of traditional gradient-based methods, and benchmark on the Max-Cut problem. We demonstrate that our Evolutionary-QAOA (E-QAOA) pairing performs on par or better than a COBYLA-based QAOA in terms of solution accuracy and variance, for $d$-3 regular graphs between 4 and 26 nodes, using both $max_count$ and Conditional Value at Risk (CVaR) for fitness function evaluations. Furthermore, we take our algorithm one step further and present a novel approach by presenting a multi-population EA distributed on two QPUs, which evolves independent and isolated populations in parallel, classically communicating elite individuals. Experiments were conducted on both simulators and IBM quantum hardware, and we investigated the relative performance accuracy and variance.