This letter to Nature (also on arXiv ) by Havlicek and coauthors deals with gaining a quantum computing advantage for classification problems and is written by quantum physicists. The main reason a friend brought this to my attention is that the classification problem is solved using support vector machines, thus fitting my recent interest in reproducing kernel Hilbert space (RKHS) methods. The main idea is that the way numerical data is encoded into a quantum state can result in a nonlinear feature map int
The main contributions over papers that are easier to read coming from an RKHS background (such as Quantum machine learning in feature Hilbert spaces by Schuld et al) are twofold. For one, Havlicek and coauthors use a feature map that does not result in a trivial/useless RKHS. Specifically they propose to use two layers of a diagonal gate and a Hadamard gate and conjecture that this gives a quantum advantage (while a single layer can be simulated classically). I am quite lost here of course without any back
The classification problem they tackle is a toy problem that they construct so as to be perfectly separable with their classification algorithm, which is of course a good sanity check for this first step of developing actual quantum machine learning. The decision of the algorithm for any of the two classes however cannot be read from the computing device deterministically, but only stochastically. The solution, seemingly common in quantum computing, is to read out the class repeatedly to obtain samples and