A nonlinear quantum neural network framework for entanglement engineering

Multipartite entanglement is a crucial resource for quantum technologies; however, its scalable generation in noisy quantum devices remains a significant challenge. Here, we propose a low-depth quantum neural network architecture with linear scaling, employing a novel approach to introducing activation functions for entanglement engineering. As a testbed to demonstrate the clear advantage unlocked by the introduction of nonlinear activations, we run a Monte Carlo sampling over $10^5$ circuit topologies for pure noiseless states. Subsequently, we focus on the noisy scenario; we employ the experimentally accessible Meyer-Wallach global entanglement as a scalable surrogate optimization cost and certify entanglement via bipartite negativity. For 10-qubit mixed states, the optimized circuits generate substantial entanglement across the bipartitions. Lastly, the presence of genuine multipartite entanglement is certified with semi-definite programming. These result establish an experimentally motivated and scalable framework for engineering multipartite entanglement on near-term quantum devices, highlighting the combined role of nonlinearity and circuit topology scaling up to 20 qubits readily.