ExMD: SU(2) matrix decomposition

In quantum information science, Berry’s geometric phase, corresponding to the evolution of the quantum system, has important information. Notably, the geometric phase is essential in developing fault-tolerant quantum computing. However, a general description of the geometric phase has not yet been reported, especially for non-commuting and non-anticommuting properties (we call these non-diabolical properties). We explain the cyclic evolution of arbitrary quantum states using multiple rotation operators with non-diabolical properties, and compare it with the quantum evolution by commuting and anticommuting properties. In addition, we analyze the conditions of such evolution in terms of geometric and dynamic phases using Uhlmann’s fidelity and visualization on the Bloch sphere, drawn in the ExMD Mathematica package.