In the context of gate-model quantum computing, atoms (or polyatomic molecules) are excited to respective Rydberg states to foster intra-gate interactions. Rydberg states with relatively high principal quantum numbers are used for relatively distant intra-gate interactions and require relatively great inter-gate separations to avoid error-inducing inter-gate interactions. Rydberg states with relatively low principal quantum numbers can be used for intra-gate interactions over relatively short intra-gate distances and require relatively small inter-gate separations to avoid error-inducing inter-gate interactions. The relatively small inter-gate separations provide opportunities for parallel gate executions, which, in turn, can provide for faster execution of the quantum circuit constituted by the gates. By using Rydberg states with relatively high principal quantum numbers where required, and Rydberg states with relatively low principal quantum numbers where possible, an optimal tradeoff between intra-gate interaction flexibility and inter-gate parallelism can be achieved.