This paper presents the first electronic structure calculation performed on a quantum computer without 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 first algorithm is the unitary coupled cluster method implemented via the variational quantum eigensolver (VQE), which predicts the correct dissociation energy to within chemical accuracy. The second algorithm is the canonical quantum algorithm for chemistry, which involves Trotterization and quantum phase estimation (PEA). The authors compare the performance of these approaches and show that VQE is robust to certain errors, suggesting that variational quantum simulations of classically intractable molecules may be viable in the near future. Quantum simulation of molecular energies is a promising application of quantum computing, as it enables numerically exact predictions of chemical reaction rates and could enable in silico design of new catalysts, pharmaceuticals, and materials. As scalable quantum hardware becomes increasingly viable, chemistry simulation has attracted significant attention due to the relatively modest number of qubits required for classically intractable molecules and the commercial value of their chemical applications. The fundamental challenge in building a quantum computer is realizing high-fidelity operations in a scalable architecture. Superconducting qubits have made rapid progress in recent years and can be fabricated in microchip foundries and manufactured at scale. Recent experiments have shown logic gate fidelities at the threshold required for quantum error correction and dynamical suppression of bit-flip errors. The authors use a device to implement and compare two quantum algorithms for chemistry. They have previously characterized their hardware using randomized benchmarking but related metrics only loosely bound how well their devices can simulate molecular energies. Thus, studying the performance of hardware on small instances of real problems is an important way to measure progress towards viable quantum computing. The authors demonstrate the variational quantum eigensolver (VQE), introduced in [19], which achieves chemical accuracy and is the first scalable quantum simulation of molecular energies performed on quantum hardware. When implemented using a unitary coupled cluster ansatz, VQE cannot be efficiently simulated classically and empirical evidence suggests that answers are accurate enough to predict chemical rates. Because VQE only requires short state preparation and measurement sequences, it has been suggested that classically intractable computations might be possible using VQE without the overhead of error correction. The authors' experiments substantiate this notion; the robustness of the VQE to systematic device errors allows the experiment to achieve chemical accuracy. The authors also report an experimental demonstration of the original quantum algorithm for chemistry, introduced in [2]. This approach involves Trotterized simulation and the quantum phase estimation algorithm. They experimentally perform this entire algorithm, including both key components, for the first time. While PEA has asymptotically better scaling in terms of precision than VQE, long and coherent gate sequences are required for its accurate implementation. The authors compare the performance of VQE and PEA, showingThis paper presents the first electronic structure calculation performed on a quantum computer without 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 first algorithm is the unitary coupled cluster method implemented via the variational quantum eigensolver (VQE), which predicts the correct dissociation energy to within chemical accuracy. The second algorithm is the canonical quantum algorithm for chemistry, which involves Trotterization and quantum phase estimation (PEA). The authors compare the performance of these approaches and show that VQE is robust to certain errors, suggesting that variational quantum simulations of classically intractable molecules may be viable in the near future. Quantum simulation of molecular energies is a promising application of quantum computing, as it enables numerically exact predictions of chemical reaction rates and could enable in silico design of new catalysts, pharmaceuticals, and materials. As scalable quantum hardware becomes increasingly viable, chemistry simulation has attracted significant attention due to the relatively modest number of qubits required for classically intractable molecules and the commercial value of their chemical applications. The fundamental challenge in building a quantum computer is realizing high-fidelity operations in a scalable architecture. Superconducting qubits have made rapid progress in recent years and can be fabricated in microchip foundries and manufactured at scale. Recent experiments have shown logic gate fidelities at the threshold required for quantum error correction and dynamical suppression of bit-flip errors. The authors use a device to implement and compare two quantum algorithms for chemistry. They have previously characterized their hardware using randomized benchmarking but related metrics only loosely bound how well their devices can simulate molecular energies. Thus, studying the performance of hardware on small instances of real problems is an important way to measure progress towards viable quantum computing. The authors demonstrate the variational quantum eigensolver (VQE), introduced in [19], which achieves chemical accuracy and is the first scalable quantum simulation of molecular energies performed on quantum hardware. When implemented using a unitary coupled cluster ansatz, VQE cannot be efficiently simulated classically and empirical evidence suggests that answers are accurate enough to predict chemical rates. Because VQE only requires short state preparation and measurement sequences, it has been suggested that classically intractable computations might be possible using VQE without the overhead of error correction. The authors' experiments substantiate this notion; the robustness of the VQE to systematic device errors allows the experiment to achieve chemical accuracy. The authors also report an experimental demonstration of the original quantum algorithm for chemistry, introduced in [2]. This approach involves Trotterized simulation and the quantum phase estimation algorithm. They experimentally perform this entire algorithm, including both key components, for the first time. While PEA has asymptotically better scaling in terms of precision than VQE, long and coherent gate sequences are required for its accurate implementation. The authors compare the performance of VQE and PEA, showing