  Quantum Hamiltonian Computing is a recent approach that uses quantum systems,
in particular a single molecule, to perform computational tasks. Within this
approach, we present explicit methods to construct logic gates using two
different designs, where the logical outputs are encoded either at fixed energy
and spatial positioning of the quantum states, or at different energies. We use
these results to construct quantum Boolean adders involving a minimal number of
quantum states with the two designs. We also establish a matrix algebra giving
an analogy between classical Boolean logic gates and quantum ones, and assess
the possibilities of both designs for more complex gates.
