Generalization in quantum machine learning from few training data

11/09/2021
by   Matthias C. Caro, et al.
21

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as √(T/N). When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to √(K / N). Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/21/2022

Out-of-distribution generalization for learning quantum dynamics

Generalization bounds are a critical tool to assess the training data re...
03/01/2022

Optimal quantum dataset for learning a unitary transformation

Unitary transformations formulate the time evolution of quantum states. ...
04/21/2022

Dynamical simulation via quantum machine learning with provable generalization

Much attention has been paid to dynamical simulation and quantum machine...
03/28/2022

Optimisation-free Classification and Density Estimation with Quantum Circuits

We demonstrate the implementation of a novel machine learning framework ...
05/23/2022

Overfitting in quantum machine learning and entangling dropout

The ultimate goal in machine learning is to construct a model function t...
09/22/2022

Structure Learning of Quantum Embeddings

The representation of data is of paramount importance for machine learni...
05/16/2022

Power and limitations of single-qubit native quantum neural networks

Quantum neural networks (QNNs) have emerged as a leading strategy to est...