A non-linear quantum neural network framework for entanglement engineering

Abstract: Multipartite entanglement is a key resource for quantum technologies, yet its scalable generation in noisy quantum devices remains challenging. Here, we propose a low-depth quantum neural network architecture with linear scaling, inspired by memory-enabled photonic components, for variational entanglement engineering. The network incorporates physically motivated non-linear activation functions, enhancing expressivity beyond linear variational circuits at fixed depth. By Monte Carlo sampling over circuit topologies, we identify architectures that efficiently generate highly entangled pure states, approaching the GHz limit, and demonstrate a clear advantage of non-linear networks up to 20 qubits. For the noisy scenario, we employ the experimentally accessible Meyer-Wallach global entanglement as a surrogate optimization cost and certify entanglement using bipartite negativity. For mixed states of up to ten qubits, the optimized circuits generate substantial entanglement across both symmetric and asymmetric bipartitions. These results establish an experimentally motivated and scalable variational framework for engineering multipartite entanglement on near-term quantum devices, highlighting the combined role of non-linearity and circuit topology.