Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks

Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices requires the optimal utilization of limited quantum resources. The commonly used gate-based QML models are convenient for software engineers, but their expressivity is restricted by the permissible circuit depth within a finite coherence time. In contrast, pulse-based models enable the construction of "infinitely" deep quantum neural networks within the same coherence time, which may unleash greater expressive power for complex learning tasks. In this paper, we investigate this potential from the perspective of quantum control theory. We first indicate that the nonlinearity of pulse-based models comes from the encoding process that can be viewed as the continuous limit of data-reuploading in gate-based models. Subsequently, we prove that the pulse-based model can approximate arbitrary nonlinear functions when the underlying physical system is ensemble controllable. Under this condition, numerical simulations show that the expressivity can be enhanced by either increasing the pulse length or the number of qubits. As anticipated, we demonstrate through numerical examples that the pulse-based model can unleash more expressive power compared to the gate-based model. These findings establish a theoretical foundation for understanding and designing expressive QML models using NISQ devices.

PAGE: Equilibrate Personalization and Generalization in Federated Learning

Federated learning (FL) is becoming a major driving force behind machine learning as a service, where customers (clients) collaboratively benefit from shared local updates under the orchestration of the service provider (server). Representing clients' current demands and the server's future demand, local model personalization and global model generalization are separately investigated, as the ill-effects of data heterogeneity enforce the community to focus on one over the other. However, these two seemingly competing goals are of equal importance rather than black and white issues, and should be achieved simultaneously. In this paper, we propose the first algorithm to balance personalization and generalization on top of game theory, dubbed PAGE, which reshapes FL as a co-opetition game between clients and the server. To explore the equilibrium, PAGE further formulates the game as Markov decision processes, and leverages the reinforcement learning algorithm, which simplifies the solving complexity. Extensive experiments on four widespread datasets show that PAGE outperforms state-of-the-art FL baselines in terms of global and local prediction accuracy simultaneously, and the accuracy can be improved by up to 35.20% and 39.91%, respectively. In addition, biased variants of PAGE imply promising adaptiveness to demand shifts in practice.