  The goal of this paper is to introduce building blocks for adiabatic quantum
algorithms. Adiabatic quantum computing uses the principle of quantum
annealing, which implies that a carefully controlled energy solution is optimal
and corresponds to minimizing a discrete function. The input function can be
influenced by rewards and penalties to favor a solution that meets restrictions
that are imposed by the problem. We show how to accomplish this influence for
gates in adiabatic quantum computing, particularly the controlled-NOT gate
(CNOT gate) which is fundamental to all quantum gates on two or more qubits. In
addition, we adapt the Toffoli gate, the Fredkin gate, and the Hadamard gate to
the Ising objective function which is a foundation for discrete optimization on
D-Wave System machines. The quantum work in this paper encompasses Boolean
operations, some of which are used to construct gates. We think the possible
advantages of the building blocks in this paper will enhance quantum algorithms
on D-Wave System computers.
