dc.contributor.author
Haferkamp, Jonas
dc.contributor.author
Montealegre-Mora, F.
dc.contributor.author
Heinrich, M.
dc.contributor.author
Eisert, Jens
dc.contributor.author
Gross, D.
dc.contributor.author
Roth, Ingo
dc.date.accessioned
2023-02-02T08:55:42Z
dc.date.available
2023-02-02T08:55:42Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/36893
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-36606
dc.description.abstract
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full n-qubit group, one often resorts to t-designs. Unitary t-designs mimic the Haar-measure up to t-th moments. It is known that Clifford operations can implement at most 3-designs. In this work, we quantify the non-Clifford resources required to break this barrier. We find that it suffices to inject O(t4log2(t)log(1/ε)) many non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an ε-approximate t-design. Strikingly, the number of non-Clifford gates required is independent of the system size – asymptotically, the density of non-Clifford gates is allowed to tend to zero. We also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators.
en
dc.format.extent
47 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Efficient Unitary Designs
en
dc.subject
System-Size Independent Number
en
dc.subject
Non-Clifford Gates
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford Gates
dc.type
Wissenschaftlicher Artikel
dc.identifier.sepid
92951
dcterms.bibliographicCitation.doi
10.1007/s00220-022-04507-6
dcterms.bibliographicCitation.journaltitle
Communications in Mathematical Physics
dcterms.bibliographicCitation.number
3
dcterms.bibliographicCitation.pagestart
995
dcterms.bibliographicCitation.pageend
1041
dcterms.bibliographicCitation.volume
397
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00220-022-04507-6
refubium.affiliation
Physik
refubium.affiliation.other
Dahlem Center für komplexe Quantensysteme
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refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
1432-0916