  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 multi-qubit 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.
