We propose quantum neural networks that include multi-qubit interactions in the neural potential leading to a reduction of the network depth without losing approximative power. We show that the presence of multiqubit potentials in the quantum perceptrons enables more efficient information processing tasks such as XOR gate implementation and prime numbers search, while it also provides a depth reduction to construct distinct entangling quantum gates like CNOT, Toffoli, and Fredkin. This simplification in the network architecture paves the way to address the connectivity challenge to scale up a quantum neural network while facilitates its training.