  We present an algorithm for finding ground states of two dimensional spin
glass systems based on ideas from matrix product states in quantum information
theory. The algorithm works directly at zero temperature and defines an
approximate "boundary Hamiltonian" whose accuracy depends on a parameter $k$.
We test the algorithm against exact methods on random field and random bond
Ising models, and we find that accurate results require a $k$ which scales
roughly polynomially with the system size. The algorithm also performs well
when tested on small systems with arbitrary interactions, where no fast, exact
algorithms exist. The time required is significantly less than Monte Carlo
schemes.
