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

• Published in: Advanced quantum technologies (Online) 2021-07, Vol.4 (7), p.n/a
• Main Authors: Yeter‐Aydeniz, Kübra, Gard, Bryan T., Jakowski, Jacek, Majumder, Swarnadeep, Barron, George S., Siopsis, George, Humble, Travis S., Pooser, Raphael C.
• Format: Article
• Language: English
• Subjects: quantum benchmarks; quantum chemistry; quantum computing; quantum imaginary time evolution; variational algorithms
• ISSN: 2511-9044; 2511-9044
• DOI: 10.1002/qute.202100012

Quantum chemistry is a key application area for noisy‐intermediate scale quantum (NISQ) 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 the performance of computing ground states for alkali‐hydrides under an array of error mitigation methods. 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 are outlined here. It is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated 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. Quantum chemistry simulation is a good test of the practical capability of today's quantum hardware. Advanced variational methods improve accuracy and reduce depth, while new algorithms such as quantum imaginary time evolution outline the growing potential, and the limitations, of near term devices in quantum simulation. Here, the performance of these algorithms on prototypical chemistry simulation problems is examined.