  Zero-noise extrapolation (ZNE) is an increasingly popular technique for
mitigating errors in noisy quantum computations without using additional
quantum resources. We review the fundamentals of ZNE and propose several
improvements to noise scaling and extrapolation, the two key components in the
technique. We introduce unitary folding and parameterized noise scaling. These
are digital noise scaling frameworks, i.e. one can apply them using only
gate-level access common to most quantum instruction sets. We also study
different extrapolation methods, including a new adaptive protocol that uses a
statistical inference framework. Benchmarks of our techniques show error
reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE
effectiveness at larger qubit numbers than have been tested previously. In
addition to presenting new results, this work is a self-contained introduction
to the practical use of ZNE by quantum programmers.
