Transfer learning of optimal QAOA parameters in combinatorial optimization

Solving combinatorial optimization problems (COPs) is a promising application ofquantum computation, with the quantum approximate optimization algorithm (QAOA)being one of the most studied quantum algorithms for solving them. However, multiple factors make the parameter search of the QAOA a hard optimization problem. Inthis work, we study transfer learning (TL), a methodology to reuse pre-trained QAOAparameters of one problem instance into different COP instances. This methodologycan be used to alleviate the necessity of classical optimization to find good parametersfor individual problems. To this end, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP),the weighted maximum cut (MaxCut) problem, the maximal independent set (MIS)problem, and portfolio optimization (PO), and find optimal β and γ parameters forp layers. We compare how well the parameters found for one problem adapt to theothers. Among the different problems, BPP is the one that produces the best transferable parameters, maintaining the probability of finding the optimal solution abovea quadratic speedup over random guessing for problem sizes up to 42 qubits andp = 10 layers. Using the BPP parameters, we perform experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of MIS instances for up to 18qubits. The results indicate that IonQ Aria yields the best overlap with the ideal probability distribution. Additionally, we show that cross-platform TL is possible using theD-Wave Advantage quantum annealer with the parameters found for BPP. We showan improvement in performance compared to the default protocols for MIS with up to170 qubits. Our results suggest that there are QAOA parameters that generalize wellfor different COPs and annealing protocols.