Visualizing quantum mechanics in an interactive simulation – Virtual Lab by Quantum Flytrap

Piotr Migdał; Klementyna Jankiewicz; Paweł Grabarz; Chiara Decaroli; Philippe Cochin

doi:10.1117/1.OE.61.8.081808

22 June 2022 Visualizing quantum mechanics in an interactive simulation – Virtual Lab by Quantum Flytrap

Piotr Migdał, Klementyna Jankiewicz, Paweł Grabarz, Chiara Decaroli, Philippe Cochin

Author Affiliations +

Optical Engineering, Vol. 61, Issue 8, 081808 (June 2022). https://doi.org/10.1117/1.OE.61.8.081808

References

1.

W. Heisenberg, Physics and Beyond, Allen & Unwin London(1971). Google Scholar

2.

A. Einstein, M. Born and H. Born, The Born-Einstein Letters: Correspondence Between Albert Einstein and Max and Hedwig Born from 1916 to 1955, New York (1971). Google Scholar

3.

M. Kim, “The Physics of Rick and Morty,” (2017) https://slate.com/technology/2017/07/rick-and-morty-gets-multiverse-theory-wrong-thats-ok.html Google Scholar

4.

D. Kaiser, How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival, Norton (2012). Google Scholar

5.

V. Scarani, L. Chua and S. Y. Liu, Six Quantum Pieces: A First Course in Quantum Physics, World Scientific(2010). Google Scholar

6.

L. Susskind and G. Hrabovsky, The Theoretical Minimum: What You Need to Know to Start Doing Physics, Basic Books, New York (2014). Google Scholar

7.

A. Matuschak and M. Nielsen, “Quantum country,” (2019) https://quantum.country Google Scholar

8.

J. R. Wootton et al., “Teaching quantum computing with an interactive textbook,” in IEEE Int. Conf. Quantum Comput. and Eng. (QCE), 385 –391 (2021). https://doi.org/10.1109/QCE52317.2021.00058 Google Scholar

9.

A. Ekert and T. Hosgood, “The online book for the Introduction to Quantum Information Science course,” (2022) https://github.com/thosgood/iqis-book Google Scholar

10.

J.-F. Bobier et al., “What happens when ‘if’ turns to ‘when’ in quantum computing?,” (2021) https://www.bcg.com/publications/2021/building-quantum-advantage Google Scholar

11.

E. Hazan et al., “The next tech revolution: quantum computing,” (2020) https://www.mckinsey.com/fr/our-insights/the-next-tech-revolution-quantum-computing Google Scholar

12.

R. Waters, “Goldman Sachs predicts quantum computing 5 years away from use in markets,” (2021) https://www.ft.com/content/bbff5dfd-caa3-4481-a111-c79f0d38d486 Google Scholar

13.

L. Nita et al., “The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving,” Res. Sci. Technol. Educ., 1 –17 (2021). https://doi.org/10.1080/02635143.2021.1920905 0263-5143 Google Scholar

14.

C. Hughes et al., “Assessing the needs of the quantum industry,” IEEE Trans. Educ., 1 –10 (2022). https://doi.org/10.1109/TE.2022.3153841 Google Scholar

15.

P. Migdał, B. Olechno and B. Podgórski, “Level generation and style enhancement – deep learning for game development overview,” (2021). Google Scholar

16.

M. Fingerhuth, T. Babej and P. Wittek, “Open source software in quantum computing,” PLOS ONE, 13 e0208561 (2018). https://doi.org/10.1371/journal.pone.0208561 POLNCL 1932-6203 Google Scholar

17.

M. Fingerhuth, “Open-source quantum software projects,” (2022). https://github.com/qosf/awesome-quantum-software Google Scholar

18.

J. R. Johansson, P. D. Nation and F. Nori, “QuTiP: an open-source Python framework for the dynamics of open quantum systems,” Comput. Phys. Commun., 183 1760 –1772 (2012). https://doi.org/10.1016/j.cpc.2012.02.021 CPHCBZ 0010-4655 Google Scholar

19.

M. S. Anis et al., “Qiskit: an open-source framework for quantum computing,” (2021). https://github.com/Qiskit/qiskit Google Scholar

20.

V. Bergholm et al., “PennyLane: automatic differentiation of hybrid quantum-classical computations,” (2020). Google Scholar

21.

N. Killoran et al., “Strawberry fields: a software platform for photonic quantum computing,” Quantum, 3 129 (2019). https://doi.org/10.22331/q-2019-03-11-129 Google Scholar

22.

H. Silvério et al., “Pulser: an open-source package for the design of pulse sequences in programmable neutral-atom arrays,” Quantum, 6 629 (2022). https://doi.org/10.22331/q-2022-01-24-629 Google Scholar

23.

M. Paltenghi and M. Pradel, “Bugs in quantum computing platforms: an empirical study,” Proc. ACM Program. Lang., 6 (OOPSLA1), 1 –27 (2022). https://doi.org/10.1145/3527330 Google Scholar

24.

J. Luo et al., “A comprehensive study of bug fixes in quantum programs,” (2022). Google Scholar

25.

Z. C. Seskir et al., “Quantum games and interactive tools for quantum technologies outreach and education,” Opt. Eng., 61 (8), 081809 (2022). https://doi.org/10.1117/1.OE.61.8.081809 Google Scholar

26.

P. Falstad, “Quantum mechanics: 1-dimensional particle states applet,” (2002) http://www.falstad.com/qm1d/ Google Scholar

27.

C. Gidney, “Quirk,” (2019) https://github.com/Strilanc/Quirk Google Scholar

28.

M. Bozzo-Rey and R. Loredo, “Introduction to the IBM Q experience and quantum computing,” in Proc. 28th Annu. Int. Conf. Comput. Sci. and Softw. Eng., CASCON ’18, 410 –412 (2018). Google Scholar

29.

B. R. La Cour et al., “The virtual quantum optics laboratory,” (2021). Google Scholar

30.

J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum, 2 79 (2018). https://doi.org/10.22331/q-2018-08-06-79 Google Scholar

31.

E. Bonawitz et al., “The double-edged sword of pedagogy: instruction limits spontaneous exploration and discovery,” Cognition, 120 322 –330 (2011). https://doi.org/10.1016/j.cognition.2010.10.001 CGTNAU 0010-0277 Google Scholar

32.

J. E. Fox, “Swinging: what young children begin to learn about physics during outdoor play,” J. Elementary Sci. Educ., 9 1 (1997). https://doi.org/10.1007/BF03173764 Google Scholar

33.

S. L. Solis, K. N. Curtis and A. Hayes-Messinger, “Children’s exploration of physical phenomena during object play,” J. Res. Childhood Educ., 31 122 –140 (2017). https://doi.org/10.1080/02568543.2016.1244583 Google Scholar

34.

J. H. M. Jensen et al., “Crowdsourcing human common sense for quantum control,” Phys. Rev. Res., 3 013057 (2021). https://doi.org/10.1103/PhysRevResearch.3.013057 PRSTCR 1554-9178 Google Scholar

35.

L. Nita et al., “Inclusive learning for quantum computing: supporting the aims of quantum literacy using the puzzle game quantum Odyssey,” (2021). Google Scholar

36.

P. Migdał et al., “Quantum Game 2,” (2020) https://github.com/Quantum-Game/quantum-game-2 Google Scholar

37.

M. Leifer, “Gamifying quantum theory,” (2017) https://digitalcommons.chapman.edu/scs_articles/541 Google Scholar

38.

P. Migdał, P. Hes and M. Krupiński, “Quantum Game with Photons,” (2016) https://github.com/stared/quantum-game Google Scholar

39.

P. Migdał et al., “Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com Google Scholar

40.

P. Migdał et al., “All user-created experiments – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/u/ Google Scholar

41.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge; New York (2010). Google Scholar

42.

C. Zendejas-Morales and P. Migdał, “Quantum logic gates for a single qubit, interactively,” (2021) https://quantumflytrap.com/blog/2021/qubit-interactively/ Google Scholar

43.

P. G. Kwiat et al., “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett., 75 4337 –4341 (1995). https://doi.org/10.1103/PhysRevLett.75.4337 PRLTAO 0031-9007 Google Scholar

44.

P. A. M. Dirac, “A new notation for quantum mechanics,” Math. Proc. Cambridge Philos. Soc., 35 416 –418 (1939). https://doi.org/10.1017/S0305004100021162 MPCPCO 0305-0041 Google Scholar

45.

W. C. Brinton, Graphic Presentation, Brinton Associates, New York City (1939). Google Scholar

46.

E. R. Tufte, The Visual Display of Quantitative Information, Graphics Press, Cheshire, Connecticut (2001). Google Scholar

47.

S. Riffle, “Understanding the Fourier transform,” (2011) https://web.archive.org/web/20130318211259/ Google Scholar

48.

Euclid and O. Byrne, (1847). Google Scholar

49.

N. Rougeux, “Byrne’s Euclid,” (2018). https://www.c82.net/euclid/ Google Scholar

50.

K. Jankiewicz and P. Migdał, “BraKetVue – a Vue-based visualization of quantum states and operations,” (2022). https://github.com/Quantum-Flytrap/bra-ket-vue Google Scholar

51.

N. F. Fernandez et al., “Clustergrammer, a web-based heatmap visualization and analysis tool for high-dimensional biological data,” Sci. Data, 4 170151 (2017). https://doi.org/10.1038/sdata.2017.151 Google Scholar

52.

J. Rodriguez-Laguna et al., “Qubism: self-similar visualization of many-body wavefunctions,” New J. Phys., 14 053028 (2012). https://doi.org/10.1088/1367-2630/14/5/053028 NJOPFM 1367-2630 Google Scholar

53.

P. Migdał, “Symmetries and self-similarity of many-body wavefunctions,” (2014). Google Scholar

54.

F. A. Farris, “Domain coloring and the argument principle,” PRIMUS, 27 827 –844 (2017). https://doi.org/10.1080/10511970.2016.1234526 1051-1970 Google Scholar

55.

G. E. P. Box and M. E. Muller, “A note on the generation of random normal deviates,” Ann. Math. Stat., 29 610 –611 (1958). https://doi.org/10.1214/aoms/1177706645 AASTAD 0003-4851 Google Scholar

56.

W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys., 75 715 –775 (2003). https://doi.org/10.1103/RevModPhys.75.715 RMPHAT 0034-6861 Google Scholar

57.

M. Schlosshauer, J. Kofler and A. Zeilinger, “A snapshot of foundational attitudes toward quantum mechanics,” Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys., 44 222 –230 (2013). https://doi.org/10.1016/j.shpsb.2013.04.004 Google Scholar

58.

S. Sivasundaram and K. H. Nielsen, “Surveying the attitudes of physicists concerning foundational issues of quantum mechanics,” (2016). Google Scholar

59.

A. A. Blanco and H. Engström, “Patterns in mainstream programming games,” Int. J. Serious Games, 7 97 –126 (2020). https://doi.org/10.17083/ijsg.v7i1.335 Google Scholar

60.

P. Migdał and P. Cochin, “Quantum Tensors – an NPM package for sparse matrix operations for quantum information and computing,” (2021) https://github.com/Quantum-Flytrap/quantum-tensors Google Scholar

61.

D. Chiang, A. M. Rush and B. Barak, “Named tensor notation,” (2021). Google Scholar

62.

C. K. Hong, Z. Y. Ou and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett., 59 2044 –2046 (1987). https://doi.org/10.1103/PhysRevLett.59.2044 Google Scholar

63.

P. Migdał et al., “Which multiphoton states are related via linear optics?,” Phys. Rev. A, 89 062329 (2014). https://doi.org/10.1103/PhysRevA.89.062329 Google Scholar

64.

V. B. Braginsky, Y. I. Vorontsov and K. S. Thorne, “Quantum nondemolition measurements,” Science, 209 547 –557 (1980). https://doi.org/10.1126/science.209.4456.547 SCIEAS 0036-8075 Google Scholar

65.

J. Nielsen, Usability Engineering, Academic Press, Boston (1993). Google Scholar

66.

S. K. Card, T. P. Moran and A. Newell, The Psychology of Human-Computer Interaction, Erlbaum, Mahwah, NJ (2008). Google Scholar

67.

J. Nielsen, “Response time limits,” (2014) https://www.nngroup.com/articles/response-times-3-important-limits/ Google Scholar

68.

K. T. Claypool and M. Claypool, “On frame rate and player performance in first person shooter games,” Multimedia Syst., 13 3 –17 (2007). https://doi.org/10.1007/s00530-007-0081-1 MUSYEW 1432-1882 Google Scholar

69.

A. Haas et al., “Bringing the web up to speed with WebAssembly,” in Proc. 38th ACM SIGPLAN Conf. Programm. Language Design and Implement., PLDI, 185 –200 (2017). https://doi.org/10.1145/3062341.3062363 Google Scholar

70.

P. Kok et al., “Review article: linear optical quantum computing,” Rev. Mod. Phys., 79 135 –174 (2007). https://doi.org/10.1103/RevModPhys.79.135 RMPHAT 0034-6861 Google Scholar

71.

M. H. Waseem and M. S. Anwar, Quantum Mechanics in the Single Photon Laboratory, IOP Publishing(2020). Google Scholar

72.

P. Migdał et al., “Experiments – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/experiments Google Scholar

73.

A. A. Michelson and E. W. Morley, “On the relative motion of the Earth and the luminiferous ether,” Am. J. Sci., s3-34 333 –345 (1887). https://doi.org/10.2475/ajs.s3-34.203.333 AJSCAP 0002-9599 Google Scholar

74.

A. Dragan, Unusually Special Relativity, World Scientific(2021). Google Scholar

75.

P. Migdał, K. Jankiewicz and P. Grabarz, “Michelson-Morley interferometer – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/michelson-morley Google Scholar

76.

P. Migdał, K. Jankiewicz and P. Grabarz, “Mach-Zehnder interferometer – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/mach-zehnder Google Scholar

77.

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C R Acad. Sci., 157 708 –710 (1913). Google Scholar

78.

P. Migdał, K. Jankiewicz and P. Grabarz, “Sagnac interferometer – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/sagnac-interferometer Google Scholar

79.

P. Migdał, K. Jankiewicz and P. Grabarz, “Three polarizer paradox – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/three-polarizer-paradox Google Scholar

80.

P. Migdał, K. Jankiewicz and P. Grabarz, (2022) https://lab.quantumflytrap.com/lab/optical-diode Google Scholar

81.

S. Lloyd, “Quantum search without entanglement,” Phys. Rev. A, 61 010301 (1999). https://doi.org/10.1103/PhysRevA.61.010301 Google Scholar

82.

B. P. Lanyon et al., “Experimental quantum computing without entanglement,” Phys. Rev. Lett., 101 200501 (2008). https://doi.org/10.1103/PhysRevLett.101.200501 PRLTAO 0031-9007 Google Scholar

83.

B. Sanguinetti et al., “Quantum random number generation on a mobile phone,” Phys. Rev. X, 4 031056 (2014). https://doi.org/10.1103/PhysRevX.4.031056 PRXHAE 2160-3308 Google Scholar

84.

S. M. Barnett and S. Croke, “Quantum state discrimination,” (2008). Google Scholar

85.

P. Migdał, K. Jankiewicz and P. Grabarz, “Nonorthogonal state discrimination – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/nonorthogonal-state-discrimination Google Scholar

86.

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys., 23 987 –997 (1993). https://doi.org/10.1007/BF00736012 FNDPA4 0015-9018 Google Scholar

87.

P. Kwiat et al., “Experimental realization of interaction-free measurements,” Ann. New York Acad. Sci., 755 (1), 383 –393 (1995). https://doi.org/10.1111/j.1749-6632.1995.tb38981.x ANYAA9 0077-8923 Google Scholar

88.

P. Migdał, K. Jankiewicz and P. Grabarz, “Elitzur-Vaidman bomb tester – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/elitzur-vaidman-bomb Google Scholar

89.

R. Hillmer and P. Kwiat, “A do-it-yourself quantum eraser,” Sci. Am., 296 (5), 90 –95 (2007). https://doi.org/10.1038/scientificamerican0507-90 SCAMAC 0036-8733 Google Scholar

90.

P. Migdał, K. Jankiewicz and P. Grabarz, “Quantum eraser – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/quantum-eraser Google Scholar

91.

P. Migdał et al., “Measurement destorys interference – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/measurement-destroys-interference Google Scholar

92.

P. Migdał, K. Jankiewicz and P. Grabarz, “Quantum Zeno effect – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/zeno-effect Google Scholar

93.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature, 299 802 –803 (1982). https://doi.org/10.1038/299802a0 Google Scholar

94.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Theor. Comput. Sci., 560 7 –11 (2014). https://doi.org/10.1016/j.tcs.2014.05.025 TCSCDI 0304-3975 Google Scholar

95.

P. Migdał et al., “BB84 quantum key distribution protocol – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/bb84 Google Scholar

96.

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. London A: Math. Phys. Sci., 439 553 –558 (1992). https://doi.org/10.1098/rspa.1992.0167 Google Scholar

97.

R. Cleve et al., “Quantum algorithms revisited,” Proc. R. Soc. London A: Math. Phys. Eng. Sci., 454 339 –354 (1998). https://doi.org/10.1098/rspa.1998.0164 Google Scholar

98.

P. Migdał et al., “Deutsch-Jozsa algorithm – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/deutsch-jozsa Google Scholar

99.

B.-G. Englert, C. Kurtsiefer and H. Weinfurter, “Universal unitary gate for single-photon 2-qubit states,” Phys. Rev. A, 63 032303 (2001). https://doi.org/10.1103/PhysRevA.63.032303 Google Scholar

100.

A. K. Ekert, “Quantum cryptography and Bell’s theorem,,” Quantum Measurements in Optics, 413 –418 Springer US, Boston, MA (1992). Google Scholar

101.

P. Migdał, K. Jankiewicz and P. Grabarz, “Ekert quantum key distribution protocol – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/ekert-protocol Google Scholar

102.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Phys. Phys. Fiz., 1 195 –200 (1964). https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195 Google Scholar

103.

J. F. Clauser et al., “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett., 23 880 –884 (1969). https://doi.org/10.1103/PhysRevLett.23.880 PRLTAO 0031-9007 Google Scholar

104.

P. Migdał, K. Jankiewicz and P. Grabarz, “CHSH Bell inequality violation – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/bell-inequality Google Scholar

105.

C. H. Bennett et al., “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett., 70 1895 –1899 (1993). https://doi.org/10.1103/PhysRevLett.70.1895 PRLTAO 0031-9007 Google Scholar

106.

P. Migdał, K. Jankiewicz and P. Grabarz, “Quantum teleportation – Virtual Lab by Quantum Flytrap,” (2022) https://lab.quantumflytrap.com/lab/quantum-teleportation Google Scholar

107.

P. Migdał, J. Rodriguez-Laguna and M. Lewenstein, “Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice,” Phys. Rev. A, 88 012335 (2013). https://doi.org/10.1103/PhysRevA.88.012335 Google Scholar

108.

D. M. Greenberger, M. A. Horne, A. Zeilinger, “Going beyond Bell’s Theorem,” Bell’s Theorem, Quantum Theory and Conceptions of the Universe, 69 –72 Springer Netherlands, Dordrecht (1989). Google Scholar

109.

J.-W. Pan et al., “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature, 403 515 –519 (2000). https://doi.org/10.1038/35000514 Google Scholar

110.

C. Foti et al., “Quantum physics literacy aimed at K12 and the general public,” Universe, 7 86 (2021). https://doi.org/10.3390/universe7040086 Google Scholar

111.

Z. Chaoui et al., “Quantecomputing für Schülerinnen und Schüler – Informatik und Gesellschaft,” (2022) https://iug.htw-berlin.de/oer_quexplained/ Google Scholar

112.

, “Shortlist | Start-up/established professional | D&AD,” (2021) https://www.dandad.org/awards/professional/2021/234167/quantum-flytrap/ Google Scholar

113.

K. Jankiewicz, P. Migdal and P. Grabarz, “Virtual Lab by Quantum Flytrap: interactive simulation of quantum mechanics,” in CHI Conf. Human Factors in Comput. Syst. Extend. Abstracts, CHI EA ’22, 1 –4 (2022). https://doi.org/10.1145/3491101.3519885 Google Scholar

114.

“QTEdu – Quantum Technology Education,” (2022) https://qtedu.eu/ Google Scholar

115.

B. Dorland et al., “Quantum physics vs. classical physics: introducing the basics with a virtual reality game,” Games and Learning Alliance, 383 –393 Springer International Publishing, Cham (2019). Google Scholar

116.

Z. Ashktorab, J. D. Weisz and M. Ashoori, “Thinking too classically: research topics in human-quantum computer interaction,” in Proc. 2019 CHI Conf. Human Factors in Comput. Syst., CHI ’19, 1 –12 (2019). https://doi.org/10.1145/3290605.3300486 Google Scholar

117.

J. D. Weisz, M. Ashoori and Z. Ashktorab, “Entanglion: a board game for teaching the principles of quantum computing,” in Proc. 2018 Annu. Symp. Comput.-Human Interaction in Play, CHI PLAY ’18, 523 –534 (2018). https://doi.org/10.1145/3242671.3242696 Google Scholar

118.

A. Parakh, P. Chundi and M. Subramaniam, “An approach towards designing problem networks in serious games,” in IEEE Conf. Games (CoG), 1 –8 (2019). https://doi.org/10.1109/CIG.2019.8848055 Google Scholar

119.

A. Parakh et al., “A novel approach for embedding and traversing problems in serious games,” in Proc. 21st Annu. Conf. Inf. Technol. Educ., SIGITE ’20, 229 –235 (2020). https://doi.org/10.1145/3368308.3415417 Google Scholar

120.

D. M. Costa, “Computational complexity of games and puzzles,” (2018). Google Scholar

121.

M. Kaur and A. Venegas-Gomez, “Defining the quantum workforce landscape: a review of global quantum education initiatives,” Opt. Eng., 61 (8), 081806 (2022). https://doi.org/10.1117/1.OE.61.8.081806 Google Scholar

122.

L. Allen, S. M. Barnett and M. J. Padgett, Optical Angular Momentum, CRC Press, S.l. (2003). Google Scholar

Access the abstract

JOURNAL ARTICLE
26 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY