Can a Quantum Computer Simulate Nuclear Magnetic Resonance Spectra Better than a Classical One?

The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem, and as such, it represents a problem for which a quantum computer may provide some practical advantage over traditional computing methods. In order to understand the extent to which such problems may provide examples of useful quantum advantage, it is important to understand the limitations of existing classical simulation methods. In this work, we benchmark our classical solver designed to solve such problems. We find that it performs well, even beyond the common experimental parameter regimes, except for a specific molecule with certain unusual features. We discuss what implications this may have for future efforts to demonstrate quantum advantage in the context of NMR.