  A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of
two different Wigner crystal orientations. In a QTR system, quantum tunneling
drives the coherent transition between the two different Wigner crystal
orientations. We theoretically study the quantum dynamics of a QTR,
particularly when the spin state of one of the ions is flipped. We show that
the quantum dynamics of an $\it{N}$-ion QTR can be described by continuous-time
cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a
magnetic field. Flipping the spin state breaks the rotational symmetry of the
QTR, making the quantum-tunneling-induced rotation distinguishable. This
symmetry breaking creates coupling between the spin state of the ions and the
rotational motion of the QTR, resulting in different quantum tunneling
dynamics.
