  Quantum computation started to become significant field of studies as it hold
great promising towards the upgrade of our current computational power.
Studying the evolution of quantum states serves as a good fundamental in
understanding quantum information which lead to quantum computation. This was
assisted with the respective mathematical tools such as Lie group and Lie
algebra. In this study, the Lie algebra of $\mathfrak{su}(8)$ is represented in
tensor product between three Pauli matrices. This is done by constructing the
generalized Gell-Mann matrices and compared to the Pauli basis. This study will
explicitly shows the one-to-one correlation of Gell-Mann matrices with the
Pauli basis resembled change of coordinates. This is particularly useful when
dealing with quantum circuit problems.
