  We show how to apply the quantum adiabatic algorithm directly to the quantum
computation of molecular properties. We describe a procedure to map electronic
structure Hamiltonians to 2-local qubit Hamiltonians with a small set of
physically realizable couplings. By combining the Bravyi-Kitaev construction to
map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to
2-local, we obtain precision requirements on the coupling strengths and a
number of ancilla qubits that scale polynomially in the problem size. Hence our
mapping is efficient. The required set of controllable interactions includes
only two types of interaction beyond the Ising interactions required to apply
the quantum adiabatic algorithm to combinatorial optimization problems. Our
mapping may also be of interest to chemists directly as it defines a dictionary
from electronic structure to spin Hamiltonians with physical interactions.
