Preparing topological projected entangled pair states on a quantum computer

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Simulating 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 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.