dc.contributor.author
Caro, Matthias C.
dc.date.accessioned
2024-08-06T13:10:53Z
dc.date.available
2024-08-06T13:10:53Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/44417
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-44129
dc.description.abstract
Learning about physical systems from quantum-enhanced experiments can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum advantages have been established for state learning, quantum process learning is less understood. We establish an exponential quantum advantage for learning an unknown n-qubit quantum process . We show that a quantum memory allows to efficiently solve the following tasks: (a) learning the Pauli transfer matrix (PTM) of an arbitrary , (b) predicting expectation values of Pauli-sparse observables measured on the output of an arbitrary upon input of a Pauli-sparse state, and (c) predicting expectation values of arbitrary observables measured on the output of an unknown with sparse PTM upon input of an arbitrary state. With quantum memory, these tasks can be solved using linearly-in-n many copies of the Choi state of . In contrast, any learner without quantum memory requires exponentially-in-n many queries, even when using adaptively designed experiments. In proving this separation, we extend existing shadow tomography bounds from states to channels. Moreover, we combine PTM learning with polynomial interpolation to learn arbitrary Hamiltonians from short-time dynamics. Our results highlight the power of quantum-enhanced experiments for learning highly complex quantum dynamics.
en
dc.format.extent
53 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Quantum channel learning
en
dc.subject
Hamiltonian learning
en
dc.subject
shadow tomography
en
dc.subject
quantum advantage
en
dc.subject
sample complexity upper bounds
en
dc.subject
query complexity lower bounds
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
14
dcterms.bibliographicCitation.doi
10.1145/3670418
dcterms.bibliographicCitation.journaltitle
ACM Transactions on Quantum Computing
dcterms.bibliographicCitation.number
2
dcterms.bibliographicCitation.volume
5
dcterms.bibliographicCitation.url
https://doi.org/10.1145/3670418
refubium.affiliation
Physik
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
2643-6817
refubium.resourceType.provider
WoS-Alert