Expressive power of parametrized quantum circuits

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

Expressive power of parametrized quantum circuits

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

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Publisher:: American Physical Society (APS)
Publication Type:: Journal Article
Citation:: Physical Review Research, 2018, 2, (3), pp. 033125
Issue Date:: 2018-10-29

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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	Tao, D https://orcid.org/0000-0001-7225-5449
dc.date.accessioned	2021-06-22T00:27:25Z
dc.date.available	2021-06-22T00:27:25Z
dc.date.issued	2018-10-29
dc.identifier.citation	Physical Review Research, 2018, 2, (3), pp. 033125
dc.identifier.issn	2643-1564
dc.identifier.issn	2643-1564
dc.identifier.uri	http://hdl.handle.net/10453/149690
dc.description.abstract	Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addition, PQCs equipped with ancillary qubits for post-selection have even stronger expressive power than those without post-selection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semi-supervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical experiments using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.
dc.language	en
dc.publisher	American Physical Society (APS)
dc.relation	http://purl.org/au-research/grants/arc/FT140100574
dc.relation	http://purl.org/au-research/grants/arc/DP180103424
dc.relation.ispartof	Physical Review Research
dc.relation.isbasedon	10.1103/physrevresearch.2.033125
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Expressive power of parametrized quantum circuits
dc.type	Journal Article
utslib.citation.volume	2
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	2021-06-22T00:27:23Z
pubs.issue	3
pubs.publication-status	Published online
pubs.volume	2
utslib.citation.issue	3

Abstract:

Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addition, PQCs equipped with ancillary qubits for post-selection have even stronger expressive power than those without post-selection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semi-supervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical experiments using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.

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http://hdl.handle.net/10453/149690