Learning bounds for quantum circuits in the agnostic setting

Popescu, Claudiu Marius

doi:10.1007/s11128-021-03225-7

Cited by 16 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, we give a comparison to previously known results. Some prior works have studied the generalization capabilities of quantum models, among them the classical learning-theoretic approaches of [81][82][83][84][85][86][87][88][89] ; the more geometric perspective of 17,18 ; and the informationtheoretic technique of 20,37 . Independently of this work, Ref.…”

Section: Discussionmentioning

confidence: 99%

Generalization in quantum machine learning from few training data

et al. 2022

View full text Add to dashboard Cite

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 $$\sqrt{T/N}$$ T / N . When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $$\sqrt{K/N}$$ 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.

show abstract

Section: Discussionmentioning

confidence: 99%

Generalization in quantum machine learning from few training data

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Thus, when training using training data D Q (N ), the out-of-distribution risk R P (α opt ) of the optimized parameters α opt after training is controlled in terms of the optimized training cost C D Q (N ) (α opt ) and the indistribution generalization error gen Q,D Q (N ) (α opt ). We can now bound the in-distribution generalization error using already known QML in-distribution generalization bounds [11][12][13][14][15][16][17][18][19][20][21][22][23] (or, indeed, any such bounds that are derived in the future). As a concrete example of guarantees that can be obtained this way, we combine Corollary 1 with an in-distribution generalization bound established in [20] to prove:…”

Section: B Out-of-distribution Generalization For Qnnsmentioning

confidence: 99%

Out-of-distribution generalization for learning quantum dynamics

Caro¹,

Huang²,

Ezzell³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The key challenge in quantum machine learning is to design models that can learn from data and apply their acquired knowledge to perform well on new data [1]. This latter ability is called generalization and has been intensely studied recently [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Constructing models that generalize well is essential for quantum machine learning tasks such as variational learning of unitaries [18][19][20][21][22][23][24], which is applied to unitary compiling [11,25,26], quantum simulation [10,27,28], quantum autoencoders [29,30] and black-hole recovery protocols [31].…”

mentioning

confidence: 99%

Generalization with quantum geometry for learning unitaries

Haug¹,

Kim²

2023

Preprint

View full text Add to dashboard Cite

Generalization is the ability of quantum machine learning models to make accurate predictions on new data by learning from training data. Here, we introduce the data quantum Fisher information metric (DQFIM) to determine when a model can generalize. For variational learning of unitaries, the DQFIM quantifies the amount of circuit parameters and training data needed to successfully train and generalize. We apply the DQFIM to explain when a constant number of training states and polynomial number of parameters are sufficient for generalization. Further, we can improve generalization by removing symmetries from training data. Finally, we show that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work opens up new approaches to improve generalization in quantum machine learning.

show abstract

Learning bounds for quantum circuits in the agnostic setting

Cited by 16 publications

References 37 publications

Generalization in quantum machine learning from few training data

Generalization in quantum machine learning from few training data

Out-of-distribution generalization for learning quantum dynamics

Generalization with quantum geometry for learning unitaries

Contact Info

Product

Resources

About