The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

References

• Backens, M., and A. Kissinger. 2018. “ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity.” arXiv:1805.02175.
   Google Scholar
• Bernstein, B. 1996. Pedagogy, Symbolic Control, and Identity: Theory, Research, Critique. London: Taylor and Francis.
   Google Scholar
• Bernstein, B. 1999. “Vertical and Horizontal Discourse: An Essay.” British Journal of Sociology of Education 20 (20): 157–173.
   Web of Science ®Google Scholar
• Bonchi, F., P. Sobocinski, and F. Zanazi. 2017. “Interacting Hopf Algebras.” Journal of Pure and Applied Algebra 221 (1): 144–184. doi:10.1016/j.jpaa.2016.06.002.
   Web of Science ®Google Scholar
• Chancellor, N., Szoke, S., Vinci, W., Aeppli, G., & Warburton, P. A. 2016. Maximum-entropy inference with a programmable annealer. Scientific Reports,6, 22318.
   PubMed Web of Science ®Google Scholar
• Coecke, B., and R. Duncan. 2011. “Interacting Quantum Observables: Categorical Algebra and Diagrammatics.” New Journal of Physics 13 (4): 043016. doi:10.1088/1367-2630/13/4/043016.
   Web of Science ®Google Scholar
• Conana, H., D. Marshall, and J. M. Case. 2016. “Exploring Pedagogical Possibilities for Transformative Approaches to Academic Literacies in Undergraduate Physics.” Critical Studies in Teaching and Learning 4 (2): 28–44. doi:10.14426/cristal.v4i2.73.
   Google Scholar
• Cooper, N. 1995. “The Epistemology of Understanding.” Inquiry 38 (3): 205–215.
   Web of Science ®Google Scholar
• Downes, L. A., A. R. MacKellar, D. J. Whiting, C. Bourgenot, C. S. Adams, and K. J. Weatherill. 2020. “Full-Field Terahertz Imaging at Kilohertz Frame Rates Using Atomic Vapor.” Physical Review 10 (1): 011027. doi:10.1103/PhysRevX.10.011027.
   Web of Science ®Google Scholar
• Eggers Bjælde, O., M. Kock Pedersen, and J. Sherson. 2015. “Gamification of Quantum Mechanics Teaching.” arXiv:1506.08128. arXiv Preprint.
   Google Scholar
• Einstein, A. 1947. “The Born-Einstein Letters; Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955. Walker, New York, 1971; Cited in Buhrman, H., Cleve, R., and Van Dam, W. 2001. Quantum Entanglement and Communication Complexity.” SIAM Journal on Computing 30 (6): 1829–1841. doi:10.1137/S0097539797324886.
   Web of Science ®Google Scholar
• Einstein, A., B. Podolsky, and N. Rosen. 1935. “Can Quantum-mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47 (10): 777. doi:10.1103/PhysRev.47.777.
   Google Scholar
• Epstein, S. 1996. Impure Science: AIDS, Activism, and the Politics of Knowledge. 7 vols. Berkeley: University of California Press.
   Google Scholar
• Grover, L. K. 1996. “A Fast Quantum Mechanical Algorithm for Database Search.” Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing: 212–219. doi:10.1145/237814.237866.
   Google Scholar
• Heck, R., O. Vuculescu, J. J. Sørensen, J. Zoller, M. G. Andreasen, M. G. Bason, and L. L. Nielsen. 2018. “Remote Optimization of an Ultracold Atoms Experiment by Experts and Citizen Scientists.” Proceedings of the National Academy of Sciences 115 (48): E11231–E11237. doi:10.1073/pnas.1716869115.
   PubMed Web of Science ®Google Scholar
• Hoffmann-Riem, H., S. Biber-Klemm, W. Grossenbacher-Mansuy, G. H. Hadorn, D. Joye, C. Pohl, D. Joye, U. Weismann, and E. Zemp. 2008. “Idea of the Handbook.” In Handbook of Transdisciplinary Research, edited by G. H. Hadorn, H. Hoffmann-Riem, S. Biber-Klemm, W. Grossenbacher-Mansuy, D. Joye, C. Pohl, D. Joye, U. Weismann, and E. Zemp, 3–17. Dordrecht: Springer.
   Google Scholar
• Hong, C. K., Z. Y. Ou, and L. Mandel. 1987. “Measurement of Subpicosecond Time Intervals between Two Photons by Interference.” Physical Review Letters 59 (18): 2044. doi:10.1103/PhysRevLett.59.2044. PMID 10035403.
   PubMed Web of Science ®Google Scholar
• Jordan, S. 2020. Quantum Algorithm Zoo. https://quantumalgorithmzoo.org/
   Google Scholar
• Kandala, A., A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta. 2017. “Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets.” Nature 549 (7671): 242–246. https://arxiv.org/pdf/1704.05018.pdf
   PubMed Web of Science ®Google Scholar
• Kendon, V. 2020. “Quantum Computing Using Continuous-time Evolution.” arXiv:2004.00704. arXiv Preprint.
   Google Scholar
• Klein, J. T. 2013. “The Transdisciplinary Moment (Um).” Integral Review 9 (2): 189–199.
   Google Scholar
• Knight, P., and I. Walmsley. 2019. “UK National Quantum Technology Programme.” Quantum Science and Technology 4 (4): 040502. doi:10.1088/2058-9565/ab4346.
   Web of Science ®Google Scholar
• Lieberoth, A., M. K. Pedersen, A. C. Marin, T. Planke, and J. F. Sherson. 2015. “Getting Humans to Do Quantum Optimization-user Acquisition, Engagement and Early Results from the Citizen Cyberscience Game Quantum Moves.” arXiv:1506.08761. arXiv Preprint.
   Google Scholar
• Lindstrøm, C. 2010. “Mapping the Hierarchy: Advancing the Theoretical and Practical Understanding of the Hierarchical Knowledge Structure of Physics.” Sixth International Basil Bernstein Symposium, Brisbane, Australia.
   Google Scholar
• Ludlow, A. D., M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt. 2015. “Optical Atomic Clocks.” Reviews of Modern Physics 87 (2): 637. doi:10.1103/RevModPhys.87.637.
   Web of Science ®Google Scholar
• Magnussen, R., S. Damgaard Hansen, K. Grønbæk, K. Mølmer, and J. Friis Sherson. 2012. “Game-based Research Collaboration Adapted to Science Education.” In Proceedings GLS 8.0 Games + Learning + Society Conference, edited by C. Martin, 431–436. Madison, Wisconsin: ETC Press.
   Google Scholar
• Maton, K. 2013. Knowledge and Knowers: Towards a Realist Sociology of Education. Abingdon: Routledge.
   Google Scholar
• Minder, M., M. Pittaluga, G. Roberts, M. Lucamarini, J. F. Dynes, Z. Yuan, and A. J. Shields. 2019. “Experimental Quantum Key Distribution beyond the Repeaterless Secret Key Capacity.” Nature Photonics 13 (5): 334–338. doi:10.1038/s41566-019-0377-7.
   Web of Science ®Google Scholar
• Montanaro, A. 2016. “Quantum Algorithms: An Overview.” Npj Quantum Information 2 (1): 1–8. doi:10.1038/npjqi.2015.23.
   Web of Science ®Google Scholar
• Moore, R., M. Arnot, J. Beck, and H. Daniels, eds. 2006. Knowledge, Power and Educational Reform: Applying the Sociology of Basil Bernstein. Abingdon: Routledge.
   Google Scholar
• Morrow, W. 1993. “Epistemological Access in the University.” AD Issues 1 (1): 3–4.
   Google Scholar
• Nowotny, H. 1993. “Socially Distributed Knowledge: Five Spaces for Science to Meet the Public.” Public Understanding of Science 2 (4): 307–319.
   Google Scholar
• O’Malley, D. 2018. “An Approach to Quantum-computational Hydrologic Inverse Analysis.” Scientific Reports 8 (1): 1–9.
   PubMed Web of Science ®Google Scholar
• QT SAB (Quantum Technologies Strategic Advisory Board). 2015. A Roadmap for Quantum Technologies in the UK. Innovate UK and Engineering and Physical Sciences Research Council. https://epsrc.ukri.org/newsevents/pubs/quantumtechroadmap/
   Google Scholar
• Roffe, J., S. Zohren, D. Horsman, and N. Chancellor. 2019. “Quantum Codes from Classical Graphical Models.” IEEE Transactions on Information Theory 66 (1): 130–146. doi:10.1109/TIT.2019.2938751.
   Web of Science ®Google Scholar
• Rosengrant, D., E. Etkina, and A. Van Heuvelen. 2007. “An Overview of Recent Research on Multiple Representations.” AIP Conference Proceedings 883 (1): 149–152. doi:10.1063/1.2508714.
   Google Scholar
• Ryle, G. 1946. Knowing How and Knowing that Gilbert Ryle: Collected Papers. 2 vols., 212–225. Salen, NH: Barnes and Noble.
   Google Scholar
• Schöbel, S., A. Janson, K. Jahn, B. Kordyaka, O. Turetken, N. Djafarova, and P. Heiberg Gad. 2020. “A Research Agenda for the Why, What, and How of Gamification Designs Results on an ECIS 2019 Panel.” Communications of the Association for Information Systems. https://www.alexandria.unisg.ch/publications/258977
   PubMed Web of Science ®Google Scholar
• Schrödinger, E. 1935. “Discussion of Probability Relations between Separated Systems.” In Mathematical Proceedings of the Cambridge Philosophical Society. 31 vols., 555–563. Cambridge: Cambridge University Press. doi:10.1017/S0305004100013554. https://doi.org/10.1017/S0305004100013554
   Google Scholar
• Shor, P. W. 1999. “Polynomial-time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer.” SIAM Review 41 (2): 303–332. doi:10.1137/S0036144598347011.
   Web of Science ®Google Scholar
• Sørensen, J. J. W., M. K. Pedersen, M. Munch, P. Haikka, J. H. Jensen, T. Planke, and J. F. Sherson. 2016. “Exploring the Quantum Speed Limit with Computer Games.” Nature 532 (7598): 210–213.
   PubMed Web of Science ®Google Scholar
• Stollenwerk, T., E. Lobe, and M. Jung. 2019. “Flight Gate Assignment with a Quantum Annealer.” International Workshop on Quantum Technology and Optimization Problems, 99–110. New York: Springer.
   Google Scholar
• Straehler-Pohl, H., and U. Gellert. 2013. “Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse.” British Journal of Sociology of Education 34 (3): 313–332. doi:10.1080/01425692.2012.714250.
   Web of Science ®Google Scholar
• Van Heuvelen, A. 1991. “Learning to Think like A Physicist: A Review of Research‐based Instructional Strategies.” American Journal of Physics 59 (10): 891–897. doi:10.1119/1.16667.
   Web of Science ®Google Scholar
• Vygotsky, L. S. 1997. The Collected Works of LS Vygotsky: Problems of the Theory and History of Psychology. 3 vols. New York: Springer.
   Google Scholar
• Wheelahan, L. 2007. How competency‐based training locks the working class out of powerful knowledge: A modified Bernsteinian analysis. British Journal of Sociology of Education, 28(5): 637–651. https://doi.org/10.1080/01425690701505540
   Web of Science ®Google Scholar
• White, J. 2012. Powerful Knowledge: Too Weak a Prop for the Traditional Curriculum. New Visions for Education Group. http://www.newvisionsforeducation.org.uk/2012/05/14/powerful-knowledge-too-weak-a-prop-for-the-traditionalcurriculum/
   Google Scholar
• Wieman, C., and K. Perkins. 2005. “Transforming Physics Education.” Physics Today 58 (11): 36. http://www.physicstoday.org/vol-58/iss-11/p36.shtml
   Web of Science ®Google Scholar
• Yates, L., and V. Millar. 2016. “‘Powerful Knowledge’ Curriculum Theories and the Case of Physics.” The Curriculum Journal 27 (3): 298–312. doi:10.1080/09585176.2016.1174141.
   Web of Science ®Google Scholar
• Young, M. 2013. “Overcoming the Crisis in Curriculum Theory: A Knowledge-based Approach.” Journal of Curriculum Studies 45 (2): 101–118. doi:10.1080/00220272.2013.764505.
   Web of Science ®Google Scholar
• Young, M., and J. Muller. 2010. “Three Educational Scenarios for the Future: Lessons from the Sociology of Knowledge.” European Journal of Education 45 (1): 11–27. doi:10.1111/j.1465-3435.2009.01413.x.
   Web of Science ®Google Scholar
• Young, M., and J. Muller. 2013. “On the Powers of Powerful Knowledge.” Review of Education 1 (3): 229–250. doi:10.1002/rev3.3017.
   Google Scholar
• Zainuddin, Z., S. K. W. Chu, M. Shujahat, and C. J. Perera. 2020. “The Impact of Gamification on Learning and Instruction: A Systematic Review of Empirical Evidence.” Educational Research Review: 100326. doi:10.1016/j.edurev.2020.100326.
   Web of Science ®Google Scholar
• Zanazi, F. 2015. “Interacting Hopf Algebras: The Theory of Linear Systems.” PhD diss., University of Lyon. https://arxiv.org/abs/1805.03032
   Google Scholar