  We show that the NP-hard quadratic unconstrained binary optimization (QUBO)
problem on a graph $G$ can be solved using an adiabatic quantum computer that
implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding
of $G$ in the quantum hardware graph $U$. There are two components to this
reduction: embedding and parameter setting. The embedding problem is to find a
minor-embedding $G^{emb}$ of a graph $G$ in $U$, which is a subgraph of $U$
such that $G$ can be obtained from $G^{emb}$ by contracting edges. The
parameter setting problem is to determine the corresponding parameters, qubit
biases and coupler strengths, of the embedded Ising Hamiltonian. In this paper,
we focus on the parameter setting problem. As an example, we demonstrate the
embedded Ising Hamiltonian for solving the maximum independent set (MIS)
problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system.
We close by discussing several related algorithmic problems that need to be
investigated in order to facilitate the design of adiabatic algorithms and AQC
architectures.
