Venn diagram showing overlap between "quantum" and "neural network"
The term "quantum neural networks" is being used with increasing frequency by the quantum computing community. Maybe as a dishonest, bait-and-switch advertising strategy, this makes sense. However, from a scientific standpoint, "quantum neural network" is a very poor name choice for what is being alluded to here.
Artificial Neural Networks, often called "Neural Nets" for short, are supposed to mimic the actual neurons in the human brain. But according to mainstream physics, human neurons are not in a quantum superposition state; there is no quantum entanglement between them. The nodes of a quantum network, on the other hand, are usually assumed to be in a quantum superposition and possess some measure of entanglement.
Furthermore, the nodes of a classical neural net are deterministic, and those of a quantum network are probabilistic, because quantum mechanics is intrinsically probabilistic.
Hence, the two terms "quantum" and "neural net" are contradictory, and non-overlapping (you could fit an aircraft carrier between them), so juxtaposing them is an oxymoron.
On the other hand, the name "Quantum Bayesian Networks" that I've been using since this 1997 paper, is not an oxymoron; it describes well what is being alluded to here, and its first usage preceded that of the term "quantum tensor network", another dishonest term being used by Google for the same thing by almost a decade.