  We present a general method to quickly generate high-fidelity control pulses
for any continuously-parameterized set of quantum gates after calibrating a
small number of reference pulses. We find that interpolating between optimized
control pulses for different quantum operations does not immediately yield a
high-fidelity intermediate operation. To solve this problem, we propose a
method to optimize control pulses specifically to provide good interpolations.
We pick several reference operations in the gate family of interest and
optimize pulses that implement these operations, then iteratively re-optimize
the pulses to guide their shapes to be similar for operations that are closely
related. Once this set of reference pulses is calibrated, we can use a
straightforward linear interpolation method to instantly obtain high-fidelity
pulses for arbitrary gates in the continuous operation space.
  We demonstrate this procedure on the three-parameter Cartan decomposition of
two-qubit gates to obtain control pulses for any arbitrary two-qubit gate (up
to single-qubit operations) with consistently high fidelity. Compared to
previous neural network approaches, the method is 7.7x more computationally
efficient to calibrate the pulse space for the set of all single-qubit gates.
Our technique generalizes to any number of gate parameters and could easily be
used with advanced pulse optimization algorithms to allow for better
translation from simulation to experiment.
