Quantum Simulation of Helium Hydride in a Solid-State Spin Register

\emph{Ab initio} computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH$^+$. Moreover, we report an energy uncertainty (given our model basis) of the order of $10^{-14}$ Hartree, which is ten orders of magnitude below desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides several important steps towards a fully scalable solid state implementation of a quantum chemistry simulator.