  The rapid progress of noisy intermediate-scale quantum (NISQ) computing
underscores the need to test and evaluate new devices and applications. Quantum
chemistry is a key application area for these devices, and therefore serves as
an important benchmark for current and future quantum computer performance.
Previous benchmarks in this field have focused on variational methods for
computing ground and excited states of various molecules, including a
benchmarking suite focused on performance of computing ground states for
alkali-hydrides under an array of error mitigation methods. Here, we outline
state of the art methods to reach chemical accuracy in hybrid quantum-classical
electronic structure calculations of alkali hydride molecules on NISQ devices
from IBM. We demonstrate how to extend the reach of variational eigensolvers
with new symmetry preserving Ans\"atze. Next, we outline how to use quantum
imaginary time evolution and Lanczos as a complementary method to variational
techniques, highlighting the advantages of each approach. Finally, we
demonstrate a new error mitigation method which uses systematic error
cancellation via hidden inverse gate constructions, improving the performance
of typical variational algorithms. These results show that electronic structure
calculations have advanced rapidly, to routine chemical accuracy for simple
molecules, from their inception on quantum computers a few short years ago, and
they point to further rapid progress to larger molecules as the power of NISQ
devices grows.
