  The power of quantum computers is still somewhat speculative. While they are
certainly faster than classical ones at some tasks, the class of problems they
can efficiently solve has not been mapped definitively onto known classical
complexity theory. This means that we do not know for which calculations there
will be a "quantum advantage," once an algorithm is found. One way to answer
the question is to find those algorithms, but finding truly quantum algorithms
turns out to be very difficult. In previous work over the past three decades we
have pursued the idea of using techniques of machine learning to develop
algorithms for quantum computing. Here we compare the performance of standard
real- and complex-valued classical neural networks with that of one of our
models for a quantum neural network, on both classical problems and on an
archetypal quantum problem: the computation of an entanglement witness. The
quantum network is shown to need far fewer epochs and a much smaller network to
achieve comparable or better results.
