With the creation of logic gates and algorithms for quantum computers and entering our lives, it is predicted that great developments will take place in this area and important efforts are made. Spin rotation processors are quantum mechanical rotation processors and have no classic counterparts. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text. In a previous paper, rotation operators for spins 1/2 to 2 were published. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin 5/2, 3 and 7/2 are worked via exponential operator for each element of related spin operators and utilizing simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators.

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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.

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