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We describe, realize, and experimentally investigate a method to performphysical rotations of ion chains, trapped in a segmented surface Paul trap, asa building block for large scale quantum computational sequences. Control oftrapping potentials is achieved by parametrizing electrode voltages in terms ofspherical harmonic potentials. Voltage sequences that enable crystal rotationsare numerically obtained by optimizing time-dependent ion positions andmotional frequencies, taking into account the effect of electrical filters inour set-up. We minimize rotation-induced heating by expanding the sequencesinto Fourier components, and optimizing the resulting parameters with amachine-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 of1.24 and 2.15 MHz. Qubit coherence loss is 0.2(2)$\%$ per rotation. We alsoinvestigate rotations of mixed species crystals ($^{40}$Ca$^+$ - $^{88}$Sr$^+$)and achieve unity success rate.

Coherent rotations of qubits within a multi-species ion-trap quantum computer