The role of cohomology in quantum computation with magic states

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buir.contributor.authorOkay, Cihan
buir.contributor.orcidOkay, Cihan|0000-0001-8097-5227
dc.citation.epage1014en_US
dc.citation.spage979
dc.citation.volumeNumber7
dc.contributor.authorRaussendorf, R.
dc.contributor.authorOkay, Cihan
dc.contributor.authorZurel, M.
dc.contributor.authorFeldmann, P.
dc.date.accessioned2024-03-12T07:50:17Z
dc.date.available2024-03-12T07:50:17Z
dc.date.issued2023-04-13
dc.departmentDepartment of Mathematics
dc.description.abstractA web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this computational scheme, the negativity of certain quasiprobability functions is an indicator for quantumness. However, when constructing quasiprobability functions to which this statement applies, a marked difference arises between the cases of even and odd local Hilbert space dimension. At a technical level, establishing negativity as an indicator of quantumness in quantum computation with magic states relies on two properties of the Wigner function: their covariance with respect to the Clifford group and positive representation of Pauli measurements. In odd dimension, Gross' Wigner function-an adaptation of the original Wigner function to odd-finite-dimensional Hilbert spaces-possesses these properties. In even dimension, Gross' Wigner function doesn't exist. Here we discuss the broader class of Wigner functions that, like Gross', are obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurements cannot be positively represented by them in any even dimension whenever the number of qudits is n ≥ 2. We establish that the obstructions to the existence of such Wigner functions are cohomological.
dc.identifier.doi10.22331/q-2023-04-13-979
dc.identifier.issn2521-327X
dc.identifier.urihttps://hdl.handle.net/11693/114545
dc.language.isoen
dc.publisherVerein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
dc.relation.isversionofhttps://dx.doi.org/10.22331/q-2023-04-13-979
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleQuantum
dc.titleThe role of cohomology in quantum computation with magic states
dc.typeArticle

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