Next Article in Journal
Symmetry in Nucleic-Acid Double Helices
Next Article in Special Issue
Representing Measurement as a Thermodynamic Symmetry Breaking
Previous Article in Journal
Asymmetry of Cerebellar Lobular Development in Ferrets
Open AccessArticle

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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop