An efficient quantum proactive incremental learning algorithm

In scenarios where a large amount of data needs to be learned, incremental learning can make full use of old knowledge, significantly reduce the computational cost of the overall learning process, and maintain high performance. In this paper, taking the MaxCut problem as our example, we introduce the idea of incremental learning into quantum computing, and propose a Quantum Proactive Incremental Learning algorithm (QPIL). Instead of a one-off training of quantum circuit, QPIL contains a multi-phase training on gradually-increased subgraphs of all vertices, proactively reducing large-scale problems to smaller ones to solve in steps, providing an efficient solution for MaxCut. Specifically, some vertices and corresponding edges are randomly selected for training to obtain optimized parameters of the quantum circuit at first. Then, in each incremental phase, the remaining vertices and corresponding edges are gradually added and the parameters obtained from the previous phase are reused in the parameter initialization of the current phase. We perform experiments on 120 different small-scale graphs, and it shows that QPIL performs superior to prevalent quantum and classical baselines in terms of approximation ratio (AR), time cost, anti-forgetting, and solving stability. In particular, QPIL’s AR surpasses 20% of mainstream quantum baselines, and the time cost is less than 1/5 of them. The idea of QPIL is expected to inspire efficient and high-quality solutions in large-scale MaxCut and other combinatorial optimization problems.