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

Quantum Hamiltonian Computing protocols for molecular electronics Boolean logic gates