  Simulating of exotic phases of matter that are not amenable to classical
techniques is one of the most important potential applications of quantum
information processing. We present an efficient algorithm for preparing a large
class of topological quantum states -- the G-injective Projected Entangled Pair
States (PEPS) -- on a quantum computer. Important examples include the resonant
valence bond (RVB) states, conjectured to be topological spin liquids. The
runtime of the algorithm scales polynomially with the condition number of the
PEPS projectors, and inverse-polynomially in the spectral gap of the PEPS
parent Hamiltonian.
