Quantum expanders from any classical Cayley graph expander

dc.creatorHarrow, Aram W.
dc.date2007-09-07
dc.date2007-10-09
dc.date.accessioned2026-07-07T09:44:20Z
dc.date.available2026-07-07T09:44:20Z
dc.descriptionWe give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap becomes the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the classical walk and the quantum Fourier transform on G are efficient. This means that using classical constant-degree constant-gap families of Cayley expander graphs on e.g. the symmetric group, we can construct efficient families of quantum expanders.
dc.description5 pages, constant gap. v2. Removed mistaken claim about QSZK. Added references including arXiv:0710.0651
dc.identifierhttps://arxiv.org/abs/0709.1142
dc.identifierhttp://arxiv.org/abs/0709.1142
dc.identifierQ. Inf. Comp., vol. 8, no. 8/9, pp. 715-721, 2008.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162837
dc.subjectQuantum Physics
dc.titleQuantum expanders from any classical Cayley graph expander
dc.typetext

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