Quantum computing with Octonions

There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an entanglement pattern. We abstract the common principle be...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Freedman, Michael, Shokrian-Zini, Modjtaba, Wang, Zhenghan
Format: Article
Language:English
Subjects:
Computation
Entanglement
Quantum computing
Online Access:Get full text
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Summary:There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an entanglement pattern. We abstract the common principle behind both approaches and find the notion of a graph or even continuous family of equiangular projections. This notion is the leading character in the paper. The largest continuous family, in a sense made precise in Corollary 4.2, is associated with the octonions and this example leads to a universal computational scheme. Adiabatic quantum computation also fits into this rubric as a limiting case: nearby projections are nearly equiangular, so as a gapped ground state space is slowly varied the corrections to unitarity are small.
ISSN:2331-8422
DOI:10.48550/arxiv.1811.08580