  A typical task for classical and quantum computing in chemistry is finding a
potential energy surface (PES) along a reaction coordinate, which involves
solving the quantum chemistry problem for many points along the reaction path.
Developing algorithms to accomplish this task on quantum computers has been an
active area of development, yet finding all the relevant eigenstates along the
reaction coordinate remains a difficult problem, and determining PESs is thus a
costly proposal. In this paper, we demonstrate the use of a eigenvector
continuation -- a subspace expansion that uses a few eigenstates as a basis --
as a tool for rapidly exploring potential energy surfaces. We apply this to
determining the binding PES or torsion PES for several molecules of varying
complexity. In all cases, we show that the PES can be captured using relatively
few basis states; suggesting that a significant amount of (quantum)
computational effort can be saved by making use of already calculated ground
states in this manner.
