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Spin-Coupling Diagrams and Incidence Geometry: A Note on Combinatorial and Quantum-Computational Aspects

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Computational Science and Its Applications – ICCSA 2016 (ICCSA 2016)

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Abstract

This paper continues previous work on quantum mechanical angular momentum theory and its applications. Relationships with projective geometry provide insight on various areas of physics and computational science. The seven-spin network previously introduced and the associate diagrams are contrasted to those of the Fano plane and its intriguing missing triad is discussed graphically. The two graphs are suggested as combinatorial and finite-geometrical “abacus” for quantum information applications, specifically for either (i)- a fermion-boson protocol, the hardware being typically a magnetic moiety distinguishing odd and even spins, or (ii)- a quantum-classical protocol, the hardware being materials (arguably molecular radicals) with both large and small angular momentum states.

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Acknowledgments

Manuela Arruda is grateful to Brazilian CNPq for a post doctoral fellowship to the Perugia University. Vincenzo Aquilanti thanks Brazilian Capes for a Special Visiting Professorship at the Bahia Federal University, and Roger Anderson (Santa Cruz, California), Ana Carla Bitencourt and Mirco Ragni (Feira de Santana, Bahia, Brazil), Robert Littlejohn (Berkeley, California), Cecilia Coletti (Chieti, Italy), Annalisa Marzuoli (Pavia, Italy) and Frederico Prudente (Salvador, Bahia, Brazil) for inspiring and productive collaborations over the years. Vincenzo Aquilanti is grateful to the support of the Italian MIUR through the SIR 2014 Grant RBSI14U3VF.

Author information

Authors and Affiliations

  1. Centro de Ciências Exatas e Tecnológicas, Universidade Federal do Recôncavo da Bahia, Cruz das Almas, Brazil

    Manuela S. Arruda

  2. Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil

    Robenilson F. Santos

  3. Instituto Federal de Alagoas, Campus Piranhas, Piranhas, Brazil

    Robenilson F. Santos

  4. Dipartmento di Chimica, Biologia and Biotecnologie, Università di Perugia, Perugia, Italy

    Manuela S. Arruda, Dimitri Marinelli & Vincenzo Aquilanti

Authors
  1. Manuela S. Arruda
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  2. Robenilson F. Santos
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  3. Dimitri Marinelli
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  4. Vincenzo Aquilanti
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Corresponding author

Correspondence to Manuela S. Arruda .

Editor information

Editors and Affiliations

  1. University of Perugia , Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata , Potenza, Italy

    Beniamino Murgante

  3. Covenant University , Ota, Nigeria

    Sanjay Misra

  4. University of Minho , Braga, Portugal

    Ana Maria A. C. Rocha

  5. Polytechnic University , Bari, Italy

    Carmelo M. Torre

  6. Monash University , Clayton, Victoria, Australia

    David Taniar

  7. Kyushu Sangyo University , Fukuoka, Japan

    Bernady O. Apduhan

  8. Saint Petersburg State University , Saint Petersburg, Russia

    Elena Stankova

  9. Beijing University of Posts & Telecommunication , Beijing, China

    Shangguang Wang

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Arruda, M.S., Santos, R.F., Marinelli, D., Aquilanti, V. (2016). Spin-Coupling Diagrams and Incidence Geometry: A Note on Combinatorial and Quantum-Computational Aspects. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_33

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  • DOI: https://doi.org/10.1007/978-3-319-42085-1_33

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