A major challenge of quantum computing is the environment. Environments are noisy and imperfect, and these imperfections cause system limitations. Yes, that statement is intentionally, and grossly, oversimplified.

The lecture I just read never used the term “neural network,” but the solution to this problem sure seems like a neural network to me.

Parameters (aka “weights”) are added to a quantum circuit to correct for environmental imperfections. An iterative loop on a classical system calculates the errors in the quantum computations and then adjusts these parameters to reduce those errors. There’s even mention of gradient descent.

Therefore, it seems that a neural network on a classical system is trained to calibrate a specific quantum system so that that quantum system can then perform other quantum calculations.

It is important to note that not every quantum circuit is a variational circuit, as described above. Ironically, however, it’s the most understandable concept of quantum computing that I’ve encountered thus far.