Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

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.