  We report the first electronic structure calculation performed on a quantum
computer without exponentially costly precompilation. We use a programmable
array of superconducting qubits to compute the energy surface of molecular
hydrogen using two distinct quantum algorithms. First, we experimentally
execute the unitary coupled cluster method using the variational quantum
eigensolver. Our efficient implementation predicts the correct dissociation
energy to within chemical accuracy of the numerically exact result. Second, we
experimentally demonstrate the canonical quantum algorithm for chemistry, which
consists of Trotterization and quantum phase estimation. We compare the
experimental performance of these approaches to show clear evidence that the
variational quantum eigensolver is robust to certain errors. This error
tolerance inspires hope that variational quantum simulations of classically
intractable molecules may be viable in the near future.
