Predicting Transferability of Optimal Parameters of Quantum Approximate Optimization Algorithm

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) have great potential for demonstrating quantum advantage. QAOA relies on the optimization of classical parameters to find the minimum energy solution. Various techniques have been proposed to avoid the direct optimization of parameters for a given instance to speed up calculations. One of the promising techniques is transferring or reusing optimal parameters of similar QAOA instances. However, defining and computing such transferability remains a challenge. In this work, we developed multiple similarity metrics that predict the transferability of optimal parameters between QAOA MaxCut instances. In these metrics, we used the parity of a graph's node degrees as well as the transferability coefficients of its constituent subgraphs. When applied to a diverse dataset of 20-node random graphs, our similarity metrics successfully predict transferability coefficients within a mean squared error of 0.0042. These metrics also explain our earlier demonstrations of successfully transferring optimal parameters of 6 node random graphs to 64 node random graphs. These findings present a pathway to use local properties of instances to speed up QAOA and other hybrid quantum-classical algorithms.