Single-shot quantum machine learning

Quantum machine learning aims to improve learning methods through the use of quantum computers. If it is to ever realize its potential, many obstacles need to be overcome. A particularly pressing one arises at the prediction stage because the outputs of quantum learning models are inherently random. This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction. In this work, we analyze when quantum learning models can evade this issue and produce predictions in a near-deterministic way - paving the way to single-shot quantum machine learning. We give a rigorous definition of single-shotness in quantum classifiers and show that the degree to which a quantum learning model is near-deterministic is constrained by the distinguishability of the embedded quantum states used in the model. Opening the black box of the embedding, we show that if the embedding is realized by quantum circuits, a certain depth is necessary for single-shotness to be even possible. We conclude by showing that quantum learning models cannot be single-shot in a generic way and trainable at the same time.