The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained hypothesis is incorrect when presented with a random input) of a quantum learning algorithm trained via pairs of input and output states when averaged over training pairs and unitaries. The bound is illustrated using a recently introduced QNN architecture.
@article{arxiv.2003.14103,
title = {No Free Lunch for Quantum Machine Learning},
author = {Kyle Poland and Kerstin Beer and Tobias J. Osborne},
journal= {arXiv preprint arXiv:2003.14103},
year = {2020}
}
Comments
8 pages, 1 figure, appendix on Haar-measure integral calculations via tensor networks