Single-shot quantum machine learning

TL;DR

This paper investigates conditions under which quantum machine learning models can produce near-deterministic predictions in a single shot, addressing a key obstacle in quantum prediction efficiency.

Contribution

It provides a rigorous definition of single-shotness for quantum classifiers and analyzes the constraints imposed by quantum state distinguishability and circuit depth.

Findings

Near-deterministic predictions depend on quantum state distinguishability.

A certain circuit depth is necessary for single-shotness in quantum embeddings.

Quantum models cannot be both single-shot and trainable in a generic setting.

Abstract

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.