No Free Lunch for Quantum Machine Learning
arXiv:2003.14103
Abstract
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.
arXiv comment8 pages, 1 figure, appendix on Haar-measure integral calculations via tensor networks
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