On the learnability of quantum neural networks

Du, Y; Hsieh, M-H; Liu, T; You, S; Tao, D

On the learnability of quantum neural networks

Du, Y Hsieh, M-H Liu, T You, S Tao, D

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Publisher:: Research Square Platform LLC
Publication Type:: Journal Article
Citation:: 2020
Issue Date:: 2020-09-25

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Field	Value	Language
dc.contributor.author	Du, Y
dc.contributor.author	Hsieh, M-H
dc.contributor.author	Liu, T
dc.contributor.author	You, S
dc.contributor.author	Tao, D
dc.date.accessioned	2023-03-13T23:04:52Z
dc.date.available	2020-09-18
dc.date.available	2023-03-13T23:04:52Z
dc.date.issued	2020-09-25
dc.identifier.citation	2020
dc.identifier.uri	http://hdl.handle.net/10453/167218
dc.description.abstract	<jats:title>Abstract</jats:title> <jats:p>Quantum neural network (QNN), or equivalently, the variational quantum circuits with a gradient-based classical optimizer, has been broadly applied to many experimental proposals for noisy intermediate scale quantum (NISQ) devices. However, the learning capability of QNN remains largely unknown due to the non-convex optimization landscape, the measurement error, and the unavoidable gate noise introduced by NISQ machines. In this study, we theoretically explore the learnability of QNN from the perspective of the trainability and generalization. Particularly, we derive the convergence performance of QNN under the NISQ setting, and identify classes of computationally hard concepts that can be efficiently learned by QNN. Our results demonstrate that large gate noise, few quantum measurements, and deep circuit depth will lead to poor convergence rates of QNN towards the empirical risk minimization. Moreover, we prove that any concept class, which is efficiently learnable by a restricted quantum statistical query (QSQ) learning model, can also be efficiently learned by QNN. Since the restricted QSQ learning model can tackle certain problems such as parity learning with a runtime speedup, our result suggests that QNN established on NISQ devices will retain the quantum advantage. Our work provides the theoretical guidance for developing advanced QNNs and opens up avenues for exploring quantum advantages using NISQ devices.</jats:p>
dc.language	en
dc.publisher	Research Square Platform LLC
dc.relation.isbasedon	10.21203/rs.3.rs-80242/v1
dc.rights	info:eu-repo/semantics/openAccess
dc.title	On the learnability of quantum neural networks
dc.type	Journal Article
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
dc.date.updated	2023-03-13T23:04:48Z
pubs.publication-status	Published

Abstract:

Abstract Quantum neural network (QNN), or equivalently, the variational quantum circuits with a gradient-based classical optimizer, has been broadly applied to many experimental proposals for noisy intermediate scale quantum (NISQ) devices. However, the learning capability of QNN remains largely unknown due to the non-convex optimization landscape, the measurement error, and the unavoidable gate noise introduced by NISQ machines. In this study, we theoretically explore the learnability of QNN from the perspective of the trainability and generalization. Particularly, we derive the convergence performance of QNN under the NISQ setting, and identify classes of computationally hard concepts that can be efficiently learned by QNN. Our results demonstrate that large gate noise, few quantum measurements, and deep circuit depth will lead to poor convergence rates of QNN towards the empirical risk minimization. Moreover, we prove that any concept class, which is efficiently learnable by a restricted quantum statistical query (QSQ) learning model, can also be efficiently learned by QNN. Since the restricted QSQ learning model can tackle certain problems such as parity learning with a runtime speedup, our result suggests that QNN established on NISQ devices will retain the quantum advantage. Our work provides the theoretical guidance for developing advanced QNNs and opens up avenues for exploring quantum advantages using NISQ devices.

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http://hdl.handle.net/10453/167218