Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states

Lumbreras, J; Haapasalo, E; Tomamichel, M

Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states

Lumbreras, J Haapasalo, E Tomamichel, M

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Publisher:: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Publication Type:: Journal Article
Citation:: Quantum, 2022, 6, pp. 749
Issue Date:: 2022-01-01

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Field	Value	Language
dc.contributor.author	Lumbreras, J
dc.contributor.author	Haapasalo, E
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.date.accessioned	2023-04-11T04:07:33Z
dc.date.available	2023-04-11T04:07:33Z
dc.date.issued	2022-01-01
dc.identifier.citation	Quantum, 2022, 6, pp. 749
dc.identifier.issn	2521-327X
dc.identifier.issn	2521-327X
dc.identifier.uri	http://hdl.handle.net/10453/169571
dc.description.abstract	We initiate the study of tradeoffs between exploration and exploitation in online learning of properties of quantum states. Given sequential oracle access to an unknown quantum state, in each round, we are tasked to choose an observable from a set of actions aiming to maximize its expectation value on the state (the reward). Information gained about the unknown state from previous rounds can be used to gradually improve the choice of action, thus reducing the gap between the reward and the maximal reward attainable with the given action set (the regret). We provide various information-theoretic lower bounds on the cumulative regret that an optimal learner must incur, and show that it scales at least as the square root of the number of rounds played. We also investigate the dependence of the cumulative regret on the number of available actions and the dimension of the underlying space. Moreover, we exhibit strategies that are optimal for bandits with a finite number of arms and general mixed states.
dc.language	en
dc.publisher	Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
dc.relation.ispartof	Quantum
dc.relation.isbasedon	10.22331/Q-2022-06-29-749
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states
dc.type	Journal Article
utslib.citation.volume	6
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access	*
dc.date.updated	2023-04-11T04:07:32Z
pubs.publication-status	Published
pubs.volume	6

Abstract:

We initiate the study of tradeoffs between exploration and exploitation in online learning of properties of quantum states. Given sequential oracle access to an unknown quantum state, in each round, we are tasked to choose an observable from a set of actions aiming to maximize its expectation value on the state (the reward). Information gained about the unknown state from previous rounds can be used to gradually improve the choice of action, thus reducing the gap between the reward and the maximal reward attainable with the given action set (the regret). We provide various information-theoretic lower bounds on the cumulative regret that an optimal learner must incur, and show that it scales at least as the square root of the number of rounds played. We also investigate the dependence of the cumulative regret on the number of available actions and the dimension of the underlying space. Moreover, we exhibit strategies that are optimal for bandits with a finite number of arms and general mixed states.

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http://hdl.handle.net/10453/169571