  While the recent demonstration of accurate computations of classically
intractable simulations on noisy quantum processors brings quantum advantage
closer, there is still the challenge of demonstrating it for practical
problems. Here we investigate the application of noisy intermediate-scale
quantum devices for simulating nuclear magnetic resonance (NMR) experiments in
the high-field regime. In this work, the NMR interactions are mapped to a
quantum device via a product formula with minimal resource overhead, an
approach that we discuss in detail. Using this approach, we show the results of
simulations of liquid-state proton NMR spectra on relevant molecules with up to
11 spins, and up to a total of 47 atoms, and compare them with real NMR
experiments. Despite current limitations, we show that a similar approach will
eventually lead to a case of quantum utility, a scenario where a practically
relevant computational problem can be solved by a quantum computer but not by
conventional means. We provide an experimental estimation of the amount of
quantum resources needed for solving larger instances of the problem with the
presented approach. The polynomial scaling we demonstrate on real processors is
a foundational step in bringing practical quantum computation closer to
reality.
