  We describe, realize, and experimentally investigate a method to perform
physical rotations of ion chains, trapped in a segmented surface Paul trap, as
a building block for large scale quantum computational sequences. Control of
trapping potentials is achieved by parametrizing electrode voltages in terms of
spherical harmonic potentials. Voltage sequences that enable crystal rotations
are numerically obtained by optimizing time-dependent ion positions and
motional frequencies, taking into account the effect of electrical filters in
our set-up. We minimize rotation-induced heating by expanding the sequences
into Fourier components, and optimizing the resulting parameters with a
machine-learning approach. Optimized sequences rotate $^{40}$Ca$^+$ -
$^{40}$Ca$^+$ crystals with axial heating rates of
$\Delta\bar{n}_{com}=0.6^{(+3)}_{(-2)}$ and $\Delta\bar{n}_{str}=3.9(5)$
phonons per rotation for the common and stretch modes, at mode frequencies of
1.24 and 2.15 MHz. Qubit coherence loss is 0.2(2)$\%$ per rotation. We also
investigate rotations of mixed species crystals ($^{40}$Ca$^+$ - $^{88}$Sr$^+$)
and achieve unity success rate.
