Figure 1. a) We seek to efficiently generate high-fidelity control pulses for continuous families of quantum gates. Here, we envision some continuous set of unitary operations between the $CNOT$ and $\sqrt{SWAP}$ operations. The goal is to efficiently obtain control pulses for any arbitrary point in this one-dimensional space of operations while only explicitly calibrating pulses at the two endpoints. b) Top: Consider some high-fidelity control pulses that implement $CNOT$ and $\sqrt{SWAP}$ (blue and red). We attempt to obtain a pulse for an intermediate operation (green) through linear interpolation. We find that interpolation yields poor results when the fixed pulses have very different shapes. Bottom: However, if we can re-optimize the pulses for $CNOT$ and $\sqrt{SWAP}$ to be more similar to each other (while still performing the correct operations), our simple linear interpolation method can obtain a high-fidelity pulse for the intermediate operation. Our methods generalize to higher-dimensional parameter spaces.