title: The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
abstract: The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
authors.affiliation: Nanosciences Group & MANA Satellite, CEMES-CNRS, 29 Rue Jeanne Marvig, F-31055 Toulouse, France.
authors.forename: G
authors.initials: G
authors.lastname: Dridi
authors.forename: R
authors.initials: R
authors.lastname: Julien
authors.forename: M
authors.initials: M
authors.lastname: Hliwa
authors.forename: C
authors.initials: C
authors.lastname: Joachim
mesh_terms: D003205:Computing Methodologies; D055641:Mathematical Concepts; D011789:Quantum Theory