Computational simulations of nuclear magnetic resonance (NMR) experiments are essential for extracting information about molecular structure and dynamics, but are often intractable on classical computers for large molecules such as proteins and protocols such as zero-field NMR. We demonstrate the first quantum simulation of a NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile on a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. Our work opens a new practical application for quantum computation, and we show how the inherent decoherence of NMR systems may enable the simulation of classically hard molecules on near-term quantum hardware.

1 aSeetharam, Kushal1 aBiswas, Debopriyo1 aNoel, Crystal1 aRisinger, Andrew1 aZhu, Daiwei1 aKatz, Or1 aChattopadhyay, Sambuddha1 aCetina, Marko1 aMonroe, Christopher1 aDemler, Eugene1 aSels, Dries uhttps://arxiv.org/abs/2109.13298