LCQNN: linear combination of quantum neural networks

Quantum neural networks (QNNs) offer a promising paradigm for quantum-enhanced machine learning, but their practical application is critically hindered by a severe trade-off between expressivity and trainability. Highly expressive models often suffer from barren plateaus, where gradients vanish exponentially, while architectures designed to avoid this issue risk becoming classically simulable, thus losing any potential for quantum advantage. To navigate this dilemma, we introduce the Linear Combination of Quantum Neural Networks (LCQNN) framework, a novel architecture inspired by the linear combination of unitaries (LCU) technique. LCQNN employs a learnable superposition of multiple QNN blocks, creating a tunable design that mitigates vanishing gradients without collapsing the model’s computational power. We provide rigorous theoretical guarantees, showing that gradient variance scales inversely with the number of combined blocks (L). We demonstrate that by adopting structured designs, such as using k-local unitaries or restricting optimization to symmetric subspaces with non-exponential dimensions, the framework ensures trainability while retaining non-trivial quantum features. Numerical experiments validate our theoretical scaling laws and demonstrate the model’s effectiveness on real-world classification tasks. Ultimately, LCQNN provides a principled and scalable methodology for designing QNNs that are both practically trainable and sufficiently powerful for tackling challenging machine learning problems.

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