  Spectroscopic mapping refers to the massive recording of spectra whilst
varying an additional degree of freedom, such as: magnetic field, location,
temperature, or charge carrier concentration. As this involves two serial
tasks, spectroscopic mapping can become excruciatingly slow. We demonstrate
exponentially faster mapping through our combination of sparse sampling and
parallel spectroscopy. We exemplify our concept using quasiparticle
interference imaging of Au(111) and Bi2Sr2CaCu2O8 (Bi2212), as two well-known
model systems. Our method is accessible, straightforward to implement with
existing scanning tunneling microscopes, and can be easily extended to enhance
gate or field-mapping spectroscopy. In view of a possible four orders of
magnitude speed advantage, it is setting the stage to fundamentally promote the
discovery of novel quantum materials.
