Preparing projected entangled pair states on a quantum computer
  We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian. 
Martin Schwarz, Kristan Temme, Frank Verstraete
quant-ph cond-mat.stat-mech cs.CC