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dc.contributor.author
Woods, Mischa P.
dc.contributor.author
Alhambra, Álvaro M.
dc.date.accessioned
2020-01-27T17:33:13Z
dc.date.available
2020-01-17T21:28:55Z
dc.date.available
2020-01-27T17:33:13Z
dc.date.issued
2019-02-20
dc.identifier.uri
http://hdl.handle.net/20.500.11850/391634
dc.description.abstract
Following the recent introduction of the task of reference frame error correction, we show how, by using reference frame alignment for clocks, near-perfect codes with a continuous Abelian group of transversal logical gates can be constructed. With this we further explore a way of circumventing the no-go theorem of Eastin and Knill, which states that if local errors are correctable, the group of transversal gates must be of finite order. We are able to do this by introducing a small error on the decoding procedure that decreases with the dimension of the frames used. Furthermore, we show that there is a direct relationship between how small this error can be and how accurate quantum clocks can be: the more accurate the clock, the smaller the error; and the no-go theorem would be violated if time could be measured perfectly in quantum mechanics. The asymptotic scaling of the error is studied under a number of scenarios of reference frames and error models. The scheme is also extended to errors at unknown locations, and we show how to achieve this by simple majority voting related error correction schemes on the reference frames. In the Outlook, we discuss our results in relation to the AdS/CFT correspondence and the Page-Wooters mechanism.
en_US
dc.language.iso
en
en_US
dc.publisher
Cornell University
en_US
dc.subject
Quantum Physics
en_US
dc.subject
Mathematical Physics
en_US
dc.title
Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames
en_US
dc.type
Working Paper
ethz.journal.title
arXiv
ethz.pages.start
1902.07725v2
en_US
ethz.size
45 p.
en_US
ethz.identifier.arxiv
1902.07725v2
ethz.publication.place
Ithaca, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
ethz.relation.isOriginalFormOf
10.3929/ethz-b-000411156
ethz.date.deposited
2020-01-17T21:29:03Z
ethz.source
BATCH
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-01-27T17:33:26Z
ethz.rosetta.lastUpdated
2020-01-27T17:33:26Z
ethz.rosetta.versionExported
true
ethz.COinS
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