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Rx, Ry and Rz Rotation Operators of Spin 4 Systems in Quantum Information Theory

Year 2022, Volume 43, Issue 3, 510 - 514, 30.09.2022
https://doi.org/10.17776/csj.1083228

Abstract

Quantum computing requires use of various physical techniques together with quantum theory. One of the promising systems is spin systems as applied and seen in pulsed nuclear magnetic resonance (NMR) and pulsed electron paramagnetic resonance (EPR) spectroscopies and hence spin-based quantum information technology.
Construction of higher spin systems and related rotation operators is important for the theoretical infrastructure that can be used in quantum information theory. It is expected that as the value of spin increases, it will give way to longer time in the computation with bigger data.
Spin operators up to spin-4 have been published in previous studies. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin-4 were worked out via exponential operator for each element of related spin operator matrices and simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. It can be predicted that quantum rotation operators for higher spins, like spin-4, will theoretically and practically contribute to spin-based quantum information technology.  

References

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  • [2] Bellac, M.A., A short Introduction To Quantum Information and Computation, (translated from French). Cambridge University Press. Berlin, (2006).
  • [3] McMahon, D., Quantum computing, Explained. John Wiley & Sons. Inc. Publication. USA, (2008) 332.
  • [4] Nakahara, M., Ohmi T., Quantum Computing From Linear Algebra to Physical Realizations, Taylor and Francis Books. Boca Raton, (2008).
  • [5] Nielsen, M.A., Chuang I. L., Quantum Computation and Quantum Information, 10th Anniversary Ed, Cambridge University Press. Cambridge, New York, (2010).
  • [6] Feynman R., Simulating physics with computers, Int. J. Theor. Phys., 21 (1982) 467–488.
  • [7] Feynman, R., Quantum Mechanical Computers, Foundation of Physics, 16(6) (1986)507.
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  • [10] Sakurai J.J., Napolitano J.J., Modern Quantum Mechanics. Cambridge University Press, United States of America, (2011).
  • [11] Schiff, L.I., Quantum Mechanics, Third Ed. New York, (1968).
  • [12] Merzbacher, E., Quantum Mechanics, Second Ed. New York, (1970).
  • [13] Morrison M.A., Parker G.A., A Guide to Rotations in Quantum Mechanics, J. Aust. Phys., 40 (1987) 465–498.
  • [14] Shu-Shen L., Gui-Lu L., Feng-Shan B., Song-Lin F., Hou-Zhi Z., Quantum computing, Proeedings of the Academy of Sciences of the United States of America, 98(21) (2001) 11847-11848.
  • [15] Blanca M.A., Flórez M., Bermejo M., Evaluation of the rotation matrices in the basis of real spherical harmonics, Journal of Molecular Structure Theochem, 419 (1997) 19-27.
  • [16] Dachsel, H., Fast and accurate determination of the Wigner rotation matrices in the fast multipole method, J. Chem.Phys., 124 (2006) 144115–1-144115–6.
  • [17] Gimbutas, Z., Greengard, L., A fast and stable method for rotating spherical harmonic expansions, J. Comput. Phys., 228 (2009) 5621–5627.
  • [18] Aubert, G., An alternative to Wigner d-matrices for rotating real spherical harmonics, AIP Advances, 3 (2013) 062121–1-062121–25.
  • [19] Tilma T., Everitt M. J., Samson J.H., Munro W.J., Nemoto K., Wigner Functions for Arbitrary Quantum Systems, Phys. Rev. Letters, 117 (2016) 180401.
  • [20] Curtright, T.L., Fairlie, D.B., Zachos, C.K., Compact Formula for Rotations as Spin Matrix Polynomials, Sıgma, 10 (2014) 1–15.
  • [21] Curtright, T.L., Van Kortryk, T.S., On Rotations as Spin Matrix Polynomials, Journal of Physics A: Mathematical and Theoretical, 48 (2014) 1-15.
  • [22] Fukushima, E., Roeder, S.B.W., Experimental pulse NMR: a nuts and bolts approach, Wesley Publishing Company, Massachusetts, (1981).
  • [23] Rule, G.S., Hitchens, T.K., Fundamentals of Protein NMR Spectroscopy, Springer. New Delhi, India, (2006).
  • [24] Oliviera I.S., Bonagamba T.J., Sarthour, R.S., Freitas, J.C.C., deAzevedo, E.R., NMR Quantum Information Processing. ElsevierScience. Netherlands, (2007).
  • [25] Jones, J.A., NMR Quantum Computation, Prog. Nucl. Magn. Reson, Spectroscopy, 38 (2001) 326–360.
  • [26] Schweiger, A., Jeschke, G., Principles of Pulse Electron Paramagnetic Resonance. Oxford University Press. UK, (2001).
  • [27] Price M.D., Fortunato E.M., Pravia M.A., Breen C., Kumaresean S., Rosenberg G., Cory D.G., Information Transfer on an NMR Quantum Information Processor, Concepts in Magnetic Resonance Part A, 13(3) (2001) 151-158.
  • [28] Govind Joshi, S.K., Spintronics and quantum computation, Indian J. Phys., 78A (3) (2004) 299-308.
  • [29] Kocakoc M., Tapramaz R., Formation of Matrices of S = 1, S = 3/2 Spin Systems in Quantum Information Theory Formation of Matrices Some Spin Systems, J. New Research in Science, 7(2) (2018) 9-12.
  • [30] Kocakoc M., Tapramaz R., Some Transactions Made with Hadamard Gate in Qutrit Systems, Journal of New Results in Engineering and Natural Science, 8 (2018) 6-10.

Year 2022, Volume 43, Issue 3, 510 - 514, 30.09.2022
https://doi.org/10.17776/csj.1083228

Abstract

References

  • [1] Gruska, J., Quantum Computing, McGraw-Hill Publishing Company. UK, (1999) 439.
  • [2] Bellac, M.A., A short Introduction To Quantum Information and Computation, (translated from French). Cambridge University Press. Berlin, (2006).
  • [3] McMahon, D., Quantum computing, Explained. John Wiley & Sons. Inc. Publication. USA, (2008) 332.
  • [4] Nakahara, M., Ohmi T., Quantum Computing From Linear Algebra to Physical Realizations, Taylor and Francis Books. Boca Raton, (2008).
  • [5] Nielsen, M.A., Chuang I. L., Quantum Computation and Quantum Information, 10th Anniversary Ed, Cambridge University Press. Cambridge, New York, (2010).
  • [6] Feynman R., Simulating physics with computers, Int. J. Theor. Phys., 21 (1982) 467–488.
  • [7] Feynman, R., Quantum Mechanical Computers, Foundation of Physics, 16(6) (1986)507.
  • [8] Wigner, E.P., Group theory and its applications to the quantum mechanics of atomic spectra, Academic Press. Los Mexico. Alamos, (1959).
  • [9] Messiah, A., Quantum Mechanics Vol. 2., North-Holland John Wiley & Sons. Orsay, France, (1966).
  • [10] Sakurai J.J., Napolitano J.J., Modern Quantum Mechanics. Cambridge University Press, United States of America, (2011).
  • [11] Schiff, L.I., Quantum Mechanics, Third Ed. New York, (1968).
  • [12] Merzbacher, E., Quantum Mechanics, Second Ed. New York, (1970).
  • [13] Morrison M.A., Parker G.A., A Guide to Rotations in Quantum Mechanics, J. Aust. Phys., 40 (1987) 465–498.
  • [14] Shu-Shen L., Gui-Lu L., Feng-Shan B., Song-Lin F., Hou-Zhi Z., Quantum computing, Proeedings of the Academy of Sciences of the United States of America, 98(21) (2001) 11847-11848.
  • [15] Blanca M.A., Flórez M., Bermejo M., Evaluation of the rotation matrices in the basis of real spherical harmonics, Journal of Molecular Structure Theochem, 419 (1997) 19-27.
  • [16] Dachsel, H., Fast and accurate determination of the Wigner rotation matrices in the fast multipole method, J. Chem.Phys., 124 (2006) 144115–1-144115–6.
  • [17] Gimbutas, Z., Greengard, L., A fast and stable method for rotating spherical harmonic expansions, J. Comput. Phys., 228 (2009) 5621–5627.
  • [18] Aubert, G., An alternative to Wigner d-matrices for rotating real spherical harmonics, AIP Advances, 3 (2013) 062121–1-062121–25.
  • [19] Tilma T., Everitt M. J., Samson J.H., Munro W.J., Nemoto K., Wigner Functions for Arbitrary Quantum Systems, Phys. Rev. Letters, 117 (2016) 180401.
  • [20] Curtright, T.L., Fairlie, D.B., Zachos, C.K., Compact Formula for Rotations as Spin Matrix Polynomials, Sıgma, 10 (2014) 1–15.
  • [21] Curtright, T.L., Van Kortryk, T.S., On Rotations as Spin Matrix Polynomials, Journal of Physics A: Mathematical and Theoretical, 48 (2014) 1-15.
  • [22] Fukushima, E., Roeder, S.B.W., Experimental pulse NMR: a nuts and bolts approach, Wesley Publishing Company, Massachusetts, (1981).
  • [23] Rule, G.S., Hitchens, T.K., Fundamentals of Protein NMR Spectroscopy, Springer. New Delhi, India, (2006).
  • [24] Oliviera I.S., Bonagamba T.J., Sarthour, R.S., Freitas, J.C.C., deAzevedo, E.R., NMR Quantum Information Processing. ElsevierScience. Netherlands, (2007).
  • [25] Jones, J.A., NMR Quantum Computation, Prog. Nucl. Magn. Reson, Spectroscopy, 38 (2001) 326–360.
  • [26] Schweiger, A., Jeschke, G., Principles of Pulse Electron Paramagnetic Resonance. Oxford University Press. UK, (2001).
  • [27] Price M.D., Fortunato E.M., Pravia M.A., Breen C., Kumaresean S., Rosenberg G., Cory D.G., Information Transfer on an NMR Quantum Information Processor, Concepts in Magnetic Resonance Part A, 13(3) (2001) 151-158.
  • [28] Govind Joshi, S.K., Spintronics and quantum computation, Indian J. Phys., 78A (3) (2004) 299-308.
  • [29] Kocakoc M., Tapramaz R., Formation of Matrices of S = 1, S = 3/2 Spin Systems in Quantum Information Theory Formation of Matrices Some Spin Systems, J. New Research in Science, 7(2) (2018) 9-12.
  • [30] Kocakoc M., Tapramaz R., Some Transactions Made with Hadamard Gate in Qutrit Systems, Journal of New Results in Engineering and Natural Science, 8 (2018) 6-10.

Details

Primary Language English
Subjects Physics, Multidisciplinary
Journal Section Natural Sciences
Authors

Mehpeyker KOCAKOÇ> (Primary Author)
CUKUROVA UNIVERSITY
0000-0001-7966-1482
Türkiye


Recep TAPRAMAZ>
ONDOKUZ MAYIS UNIVERSITY
0000-0002-7051-1717
Türkiye

Publication Date September 30, 2022
Application Date March 5, 2022
Acceptance Date July 1, 2022
Published in Issue Year 2022, Volume 43, Issue 3

Cite

APA Kocakoç, M. & Tapramaz, R. (2022). Rx, Ry and Rz Rotation Operators of Spin 4 Systems in Quantum Information Theory . Cumhuriyet Science Journal , 43 (3) , 510-514 . DOI: 10.17776/csj.1083228