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

Archit Dhingra

doi:10.2478/qic-2025-0040

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.

References

M. A. Nielsen and I. L. Chuang (2010). Quantum Computation and Quantum Information, Cambridge University Press, Cambridge.
Search in Google Scholar Back to article
F. Bloch (1951). Physica, 17, 272–281.
Search in Google Scholar Back to article
C. E. Shannon (1948). Bell System Technical Journal, 27, 379–423.
Search in Google Scholar Back to article
I. Bengtsson and K. Zyczkowski (2017). Geometry of Quantum States, Cambridge University Press, Cambridge.
Search in Google Scholar Back to article
J. Von Neumann (1996). Mathematical Foundations of Quantum Mechanics, Princeton University Press.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
I. Bengtsson and K. Zyczkowski (2017). Geometry of Quantum States, Cambridge University Press, Cambridge.
Search in Google Scholar Back to article
C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters (1993). Physical Review Letters, 70, 1895–1899.
Search in Google Scholar Back to article
D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger (1997). Nature, 390, 575–579.
Search in Google Scholar Back to article
F. Grosshans and P. Grangier (2001). Physical Review A - Atomic, Molecular, and Optical Physics, 64, 4.
Search in Google Scholar Back to article
A. K. Pati and S. L. Braunstein (2000). Nature,404, 164–165.
Search in Google Scholar Back to article
A. Kalev and I. Hen (2008). Physical Review Letters, 100, 210502.
Search in Google Scholar Back to article
D. Coppersmith, arXiv (2002). DOI: https://doi.org/10.48550/arXiv.quant-ph/0201067.
Search in Google Scholar Back to article
A. Ekert, P. M. Hayden and H. Inamori (2007). In Coherent atomic matter waves, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 661–701.
Search in Google Scholar Back to article
J. Wen, S. Cong and X. Zou (2012). Proceedings of the World Congress on Intelligent Control and Automation (WCICA), 5096–5101.
Search in Google Scholar Back to article
D. Deutsch, A. Barenco and A. Ekert (1995). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 449, 669–677.
Search in Google Scholar Back to article
A. Barenco, C. H. Bennett, R. Cleve, D. P. Divincenzo, N. Margolus, P. Shor et al. (1995). Physical Review A, 52, 3457–3467.
Search in Google Scholar Back to article
S. L. Braunstein, A. Mann and M. Revzen (1992). Physical Review Letters, 68, 3259–3261.
Search in Google Scholar Back to article
C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher (1996). Physical Review A, 53, 2046–2052.
Search in Google Scholar Back to article
H. J. Briegel and R. Raussendorf (2001). Physical Review Letters, 86, 910–913.
Search in Google Scholar Back to article
D. Sych and G. Leuchs (2009). New Journal of Physics, 11, 013006.
Search in Google Scholar Back to article
M. Mosca (2012). Computational Complexity: Theory, Techniques, and Applications, 9781461418, 2303–2333.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
D. Deutsch and R. Jozsa (1992). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 439, 553–558.
Search in Google Scholar Back to article
D. Deutsch (1985). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 400, 97–117.
Search in Google Scholar Back to article
E. Bernstein and U. Vazirani (1997). SIAM Journal on Computing, 26, 1411–1473.
Search in Google Scholar Back to article
P. W. Shor (2002). In Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc. Press, pp. 124–134.
Search in Google Scholar Back to article
L. K. Grover (1997). Physical Review Letters, 79, 325–328.
Search in Google Scholar Back to article
E. Grumbling and M. Horowitz (2019). Eds., Quantum Computing, National Academies Press, Washington, D.C.
Search in Google Scholar Back to article
R. Müller and F. Greinert (2023). Quantum Technologies: For Engineers, 1–216.
Search in Google Scholar Back to article
C. Bernhardt (2019). Quantum Computing for Everyone, The MIT Press.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
J. Bley, E. Rexigel, A. Arias, N. Longen, L. Krupp, M. Kiefer-Emmanouilidis et al. (2024). Phys Rev Res, 6, 023077.
Search in Google Scholar Back to article

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

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