Quantum annealing (QA) has attracted research interest as a sampler and combinatorial optimization problem (COP) solver. A recently proposed sampling-based solver for QA significantly reduces the required number of qubits, being capable of large COPs. In relation to this, a trainable sampling-based COP solver has been proposed that optimizes its internal parameters from a dataset by using a deep learning technique called deep unfolding. Although learning the internal parameters accelerates the convergence speed, the sampler in the trainable solver is restricted to using a classical sampler owing to the training cost. In this study, to utilize QA in the trainable solver, we propose classical-quantum transfer learning, where parameters are trained classically, and the trained parameters are used in the solver with QA. The results of numerical experiments demonstrate that the trainable quantum COP solver using classical-quantum transfer learning improves convergence speed and execution time over the original solver.

The emerging classical-quantum transfer learning paradigm has brought a decent performance to quantum computational models in many tasks, such as computer vision, by enabling a combination of quantum models and classical pre-trained neural networks. However, using quantum computing with pre-trained models has yet to be explored in natural language processing (NLP). Due to the high linearity constraints of the underlying quantum computing infrastructures, existing Quantum NLP models are limited in performance on real tasks. We fill this gap by pretraining a sentence state with complex-valued BERT-like architecture, and adapting it to the classical-quantum transfer learning scheme for sentence classification. On quantum simulation experiments, the pre-trained representation can bring 50% to 60% increases to the capacity of end-to-end quantum models. Quantum computing combines quantum mechanics and computer science. The concepts of superposition and entanglement bring inherent parallelism between qubits, the basic computational element, which endow enormous computational power to quantum devices. Classical-quantum transfer learning (Mari et al., 2020) has emerged as an appealing quantum machine learning technique.