Quantum Computation and Measurements from an Exotic Space-Time $R^4$ - CNRS - Centre national de la recherche scientifique
Article Dans Une Revue Symmetry Année : 2020

Quantum Computation and Measurements from an Exotic Space-Time $R^4$

Raymond Aschheim
Marcelo M. Amaral
  • Fonction : Auteur
Klee Irwin

Résumé

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’.

Dates et versions

hal-02628108 , version 1 (26-05-2020)

Identifiants

Citer

Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin. Quantum Computation and Measurements from an Exotic Space-Time $R^4$. Symmetry, 2020, 12 (5), pp.736. ⟨10.3390/sym12050736⟩. ⟨hal-02628108⟩
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