  Quantum chemistry simulations on a quantum computer suffer from the overhead
needed for encoding the fermionic problem in a bosonic system of qubits. By
exploiting the block diagonality of a fermionic Hamiltonian, we show that the
number of required qubits can be reduced by a factor of two or more. There is
no need to go into the basis of the Hilbert space for this reduction because
all operations can be performed in the operator space. The scheme is conceived
as a pre-computational step that would be performed on a classical computer
prior to the actual quantum simulation. We apply this scheme to reduce the
number of qubits necessary to simulate both the Hamiltonian of the two-site
Fermi-Hubbard model and the hydrogen molecule. Both quantum systems can then be
simulated with a two-qubit quantum computer.
