Quantum federated learning (QFL) is a quantum extension of the classical federated learning model across multiple local quantum devices. An efficient optimization algorithm is always expected to minimize the communication overhead among different quantum participants. In this work, we propose an efficient optimization algorithm, namely federated quantum natural gradient descent (FQNGD), and further, apply it to a QFL framework that is composed of a variational quantum circuit (VQC)-based quantum neural networks (QNN). Compared with stochastic gradient descent methods like Adam and Adagrad, the FQNGD algorithm admits much fewer training iterations for the QFL to get converged. Moreover, it can significantly reduce the total communication overhead among local quantum devices. Our experiments on a handwritten digit classification dataset justify the effectiveness of the FQNGD for the QFL framework in terms of a faster convergence rate on the training set and higher accuracy on the test set.

This work investigates an extension of transfer learning applied in machine learning algorithms to the emerging hybrid end-to-end quantum neural network (QNN) for spoken command recognition (SCR). Our QNN-based SCR system is composed of classical and quantum components: (1) the classical part mainly relies on a 1D convolutional neural network (CNN) to extract speech features; (2) the quantum part is built upon the variational quantum circuit with a few learnable parameters. Since it is inefficient to train the hybrid end-to-end QNN from scratch on a noisy intermediate-scale quantum (NISQ) device, we put forth a hybrid transfer learning algorithm that allows a pre-trained classical network to be transferred to the classical part of the hybrid QNN model. The pre-trained classical network is further modified and augmented through jointly fine-tuning with a variational quantum circuit (VQC). The hybrid transfer learning methodology is particularly attractive for the task of QNN-based SCR because low-dimensional classical features are expected to be encoded into quantum states. We assess the hybrid transfer learning algorithm applied to the hybrid classical-quantum QNN for SCR on the Google speech command dataset, and our classical simulation results suggest that the hybrid transfer learning can boost our baseline performance on the SCR task.