The paper reports the first electronic structure calculation performed on a quantum computer without the need for exponentially costly precompilation. The authors use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms: the variational quantum eigensolver (VQE) and the canonical quantum algorithm for chemistry, which involves Trotterization and quantum phase estimation (PEA). The VQE experiment achieves chemical accuracy, predicting the correct dissociation energy within the numerical exact result. The PEA experiment, while showing better asymptotic scaling in precision, requires long and coherent gate sequences. The robustness of the VQE to systematic device errors is highlighted, suggesting that it may be more resilient to errors in pre-error corrected quantum computing compared to traditional gate model algorithms. The results inspire hope that VQE can provide solutions to classically intractable problems even without error correction.The paper reports the first electronic structure calculation performed on a quantum computer without the need for exponentially costly precompilation. The authors use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms: the variational quantum eigensolver (VQE) and the canonical quantum algorithm for chemistry, which involves Trotterization and quantum phase estimation (PEA). The VQE experiment achieves chemical accuracy, predicting the correct dissociation energy within the numerical exact result. The PEA experiment, while showing better asymptotic scaling in precision, requires long and coherent gate sequences. The robustness of the VQE to systematic device errors is highlighted, suggesting that it may be more resilient to errors in pre-error corrected quantum computing compared to traditional gate model algorithms. The results inspire hope that VQE can provide solutions to classically intractable problems even without error correction.