Transferring QAOA parameters from small instances to large

The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for  achieving quantum advantage through quantum-enhanced combinatorial optimization. However, finding optimal parameters to run QAOA is a hard problem that is usually tackled by variational loop, i.e., the circuit is executed with the current parameters on a quantum device, and then the parameters are updated on a classical device. Such variational loops are extremely time consuming. In our recent paper we find the QAOA parameters for small optimization instances and transfer them to the larger ones accelerating the entire process.

Alexey Galda, Xiaoyuan Liu, Danylo Lykov, Yuri Alexeev, Ilya Safro "Transferability of optimal QAOA parameters between random graphs", IEEE International Conference on Quantum Computing and Engineering (QCE), preprint at https://arxiv.org/pdf/2106.07531.pdf, 2021

In a typical  QAOA setup, a set of quantum circuit parameters is optimized to prepare a quantum state used to find the optimal solution of a combinatorial optimization problem. Several empirical observations about optimal parameter concentration effects for special QAOA MaxCut problem instances have been made in recent literature, however, a rigorous study of the subject is still lacking. We show that convergence of the optimal QAOA parameters around specific values and, consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on the local properties of the graphs, specifically the types of subgraphs (lightcones) from which the graphs are composed. We apply this approach to random regular and general random graphs. For example, we demonstrate how optimized parameters calculated for a 6-node random graph can be successfully used without modification as nearly optimal parameters for a 64-node random graph, with less than 1% reduction in approximation ratio as a result. This work presents a pathway to identifying classes of combinatorial optimization instances for which such variational quantum algorithms as QAOA can be substantially accelerated.