{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:44:45Z","timestamp":1760402685849,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T00:00:00Z","timestamp":1588636800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 \u2018magic\u2019 state     \u03c8     in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite \u2018contextual\u2019 geometry. In the present work, we choose G as the fundamental group      \u03c0 1   ( V )      of an exotic 4-manifold V, more precisely a \u2018small exotic\u2019 (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\u2019s 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 \u2018quantum gravity\u2019.<\/jats:p>","DOI":"10.3390\/sym12050736","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T04:46:07Z","timestamp":1588826767000},"page":"736","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Quantum Computation and Measurements from an Exotic Space-Time R4"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5739-546X","authenticated-orcid":false,"given":"Michel","family":"Planat","sequence":"first","affiliation":[{"name":"Institut FEMTO-ST CNRS UMR 6174, Universit\u00e9 de Bourgogne\/Franche-Comt\u00e9, 15 B Avenue des Montboucons, F-25044 Besan\u00e7on, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6953-8202","authenticated-orcid":false,"given":"Raymond","family":"Aschheim","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0637-1916","authenticated-orcid":false,"given":"Marcelo M.","family":"Amaral","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]},{"given":"Klee","family":"Irwin","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"170387","DOI":"10.1098\/rsos.170387","article-title":"Magic informationally complete POVMs with permutations","volume":"4","author":"Planat","year":"2017","journal-title":"R. 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