Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits. We discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk for instantaneous spectral diffusion (ISD). Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of 2.1 ×10−4 when ISD is not considered and 3.4 ×10−4 when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from 5 ×10−4→3 ×10−3 over a broad range of dipole-dipole interaction strengths.