Quantum Information & Computation
Volume 25, Issue 6
RESEARCH ARTICLE Open access

Quantum Information and Computing for Beginners: Basics of Qubit Transformations and Quantum Algorithms

Archit Dhingra

Author affiliations
  • Archit Dhingra1
  1. FinEstBeAMS, MAX IV Laboratory, Fotongatan 2, Lund, Sweden

pp. 773-783 · 10.2478/qic-2025-0040

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Abstract

Quantum information and quantum computing are based on the concept and manipulation of qubits. In this pedagogical Tutorial–written with the aim of assisting self-motivated undergraduate mathematics, physics, and engineering students–transformation of these qubits, especially the Hadamard transformation (H) and the phase shifter transformation (Φ), is illustrated. Two-qubit gates and their application in production of entangled states, along with quantum algorithms (including Deutsch–Jozsa algorithm), are included as well. With 2025 being declared as the International Year of Quantum Science and Technology (IYQ) by the United Nations General Assembly (UNGA), under the leadership of United Nations Educational, Scientific and Cultural Organization (UNESCO), the timeliness and relevance of this Tutorial, in order to nudge the budding researchers in the “quantum” direction, cannot be emphasized enough.
Open accessCC BY-NC-ND 4.0

Keywords

  • Hilbert space
  • Bloch sphere
  • quantum entanglement
  • quantum algorithm
  • quantum parallelism
  • succinct quantum computing tutorial for university students

Suggested citation

Archit Dhingra (2025). Quantum Information and Computing for Beginners: Basics of Qubit Transformations and Quantum Algorithms. Quantum Information & Computation, 25(6), 773-783. https://doi.org/10.2478/qic-2025-0040

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References (33)

  1. M. A. Nielsen and I. L. Chuang (2010). Quantum Computation and Quantum Information, Cambridge University Press, Cambridge.Google Scholar
  2. F. Bloch (1951). Physica, 17, 272–281.DOI: 10.1016/0031-8914(51)90068-7Google Scholar
  3. C. E. Shannon (1948). Bell System Technical Journal, 27, 379–423.DOI: 10.1002/j.1538-7305.1948.tb01338.xGoogle Scholar
  4. I. Bengtsson and K. Zyczkowski (2017). Geometry of Quantum States, Cambridge University Press, Cambridge.Google Scholar
  5. J. Von Neumann (1996). Mathematical Foundations of Quantum Mechanics, Princeton University Press.Google Scholar
  6. R. K. Pathria and P. D. Beale (2011). In Statistical Mechanics (Third Edition), eds. R. K. Pathria and P. D. Beale, Academic Press, Boston, Third Edit., pp. 39–90.DOI: 10.1016/B978-0-12-382188-1.00003-7Google Scholar
  7. I. Bengtsson and K. Zyczkowski (2017). Geometry of Quantum States, Cambridge University Press, Cambridge.Google Scholar
  8. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters (1993). Physical Review Letters, 70, 1895–1899.DOI: 10.1103/PhysRevLett.70.1895Google Scholar
  9. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger (1997). Nature, 390, 575–579.DOI: 10.1038/37539Google Scholar
  10. F. Grosshans and P. Grangier (2001). Physical Review A - Atomic, Molecular, and Optical Physics, 64, 4.DOI: 10.1103/PhysRevA.64.010301Google Scholar
  11. A. K. Pati and S. L. Braunstein (2000). Nature,404, 164–165.DOI: 10.1038/35004532Google Scholar
  12. A. Kalev and I. Hen (2008). Physical Review Letters, 100, 210502.DOI: 10.1103/PhysRevLett.100.210502Google Scholar
  13. D. Coppersmith, arXiv (2002). DOI: https://doi.org/10.48550/arXiv.quant-ph/0201067.Google Scholar
  14. A. Ekert, P. M. Hayden and H. Inamori (2007). In Coherent atomic matter waves, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 661–701.Google Scholar
  15. J. Wen, S. Cong and X. Zou (2012). Proceedings of the World Congress on Intelligent Control and Automation (WCICA), 5096–5101.DOI: 10.1109/WCICA.2012.6359443Google Scholar
  16. D. Deutsch, A. Barenco and A. Ekert (1995). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 449, 669–677.DOI: 10.1098/rspa.1995.0065Google Scholar
  17. A. Barenco, C. H. Bennett, R. Cleve, D. P. Divincenzo, N. Margolus, P. Shor et al. (1995). Physical Review A, 52, 3457–3467.DOI: 10.1103/PhysRevA.52.3457Google Scholar
  18. S. L. Braunstein, A. Mann and M. Revzen (1992). Physical Review Letters, 68, 3259–3261.DOI: 10.1103/PhysRevLett.68.3259Google Scholar
  19. C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher (1996). Physical Review A, 53, 2046–2052.DOI: 10.1103/PhysRevA.53.2046Google Scholar
  20. H. J. Briegel and R. Raussendorf (2001). Physical Review Letters, 86, 910–913.DOI: 10.1103/PhysRevLett.86.910Google Scholar
  21. D. Sych and G. Leuchs (2009). New Journal of Physics, 11, 013006.DOI: 10.1088/1367-2630/11/1/013006Google Scholar
  22. M. Mosca (2012). Computational Complexity: Theory, Techniques, and Applications, 9781461418, 2303–2333.DOI: 10.1007/978-1-4614-1800-9_144Google Scholar
  23. R. Cleve, A. Ekert, C. Macchiavello and M. Mosca (1998). Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454, 339–354.DOI: 10.1098/rspa.1998.0164Google Scholar
  24. D. Deutsch and R. Jozsa (1992). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 439, 553–558.DOI: 10.1098/rspa.1992.0167Google Scholar
  25. D. Deutsch (1985). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 400, 97–117.DOI: 10.1098/rspa.1985.0070Google Scholar
  26. E. Bernstein and U. Vazirani (1997). SIAM Journal on Computing, 26, 1411–1473.DOI: 10.1137/S0097539796300921Google Scholar
  27. P. W. Shor (2002). In Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc. Press, pp. 124–134.Google Scholar
  28. L. K. Grover (1997). Physical Review Letters, 79, 325–328.DOI: 10.1103/PhysRevLett.79.325Google Scholar
  29. E. Grumbling and M. Horowitz (2019). Eds., Quantum Computing, National Academies Press, Washington, D.C.DOI: 10.17226/25196Google Scholar
  30. R. Müller and F. Greinert (2023). Quantum Technologies: For Engineers, 1–216.DOI: 10.1515/9783110717457Google Scholar
  31. C. Bernhardt (2019). Quantum Computing for Everyone, The MIT Press.DOI: 10.7551/mitpress/11860.001.0001Google Scholar
  32. C. Hughes, J. Isaacson, A. Perry, R. F. Sun and J. Turner. Quantum Computing for the Quantum Curious, DOI:https://doi.org/10.1007/978-3-030-61601-4.DOI: 10.1007/978-3-030-61601-4Google Scholar
  33. J. Bley, E. Rexigel, A. Arias, N. Longen, L. Krupp, M. Kiefer-Emmanouilidis et al. (2024). Phys Rev Res, 6, 023077.DOI: 10.1103/PhysRevResearch.6.023077Google Scholar