LCQNN: Linear Combination of Quantum Neural Networks

Abstract

Quantum neural networks combine quantum computing with advanced data-driven methods, offering promising applications in quantum machine learning. However, the optimal paradigm for balancing trainability and expressivity in QNNs remains an open question. To address this, we introduce the Linear Combination of Quantum Neural Networks (LCQNN) framework, which uses the linear combination of unitaries concept to create a tunable design that mitigates vanishing gradients without incurring excessive classical simulability. We show how specific structural choices, such as adopting $k$-local control unitaries or restricting the model to certain group-theoretic subspaces, prevent gradients from collapsing while maintaining sufficient expressivity for complex tasks. We further employ the LCQNN model to handle supervised learning tasks, demonstrating its effectiveness on real datasets. In group action scenarios, we show that by exploiting symmetry and excluding exponentially large irreducible subspaces, the model circumvents barren plateaus. Overall, LCQNN provides a novel framework for focusing quantum resources into architectures that are practically trainable yet expressive enough to tackle challenging machine learning applications.