Rx, Ry and Rz Rotation Operators of Spin 4 Systems in Quantum Information Theory
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.
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.
Keywords
Rotation operator, Spin, Quantum computers, Quantum information theory, Linear curve fitting process.
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).