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Article

Quantum Computation and Measurements from an Exotic Space-Time R4

1
Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
2
Quantum Gravity Research, Los Angeles, CA 90290, USA
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 736; https://doi.org/10.3390/sym12050736
Received: 17 March 2020 / Revised: 3 April 2020 / Accepted: 16 April 2020 / Published: 5 May 2020
(This article belongs to the Special Issue Symmetry in Quantum Systems)
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state ψ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite ‘contextual’ geometry. In the present work, we choose G as the fundamental group π 1 ( V ) of an exotic 4-manifold V, more precisely a ‘small exotic’ (space-time) R 4 (that is homeomorphic and isometric, but not diffeomorphic to the Euclidean R 4 ). Our selected example, due to S. Akbulut and R. E. Gompf, has two remarkable properties: (a) it shows the occurrence of standard contextual geometries such as the Fano plane (at index 7), Mermin’s pentagram (at index 10), the two-qubit commutation picture G Q ( 2 , 2 ) (at index 15), and the combinatorial Grassmannian Gr ( 2 , 8 ) (at index 28); and (b) it allows the interpretation of MICs measurements as arising from such exotic (space-time) R 4 s. Our new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of ‘quantum gravity’. View Full-Text
Keywords: topological quantum computing; 4-manifolds; akbulut cork; exotic R4; fundamental group; finite geometry; Cayley–Dickson algebras topological quantum computing; 4-manifolds; akbulut cork; exotic R4; fundamental group; finite geometry; Cayley–Dickson algebras
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MDPI and ACS Style

Planat, M.; Aschheim, R.; Amaral, M.M.; Irwin, K. Quantum Computation and Measurements from an Exotic Space-Time R4. Symmetry 2020, 12, 736. https://doi.org/10.3390/sym12050736

AMA Style

Planat M, Aschheim R, Amaral MM, Irwin K. Quantum Computation and Measurements from an Exotic Space-Time R4. Symmetry. 2020; 12(5):736. https://doi.org/10.3390/sym12050736

Chicago/Turabian Style

Planat, Michel; Aschheim, Raymond; Amaral, Marcelo M.; Irwin, Klee. 2020. "Quantum Computation and Measurements from an Exotic Space-Time R4" Symmetry 12, no. 5: 736. https://doi.org/10.3390/sym12050736

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