%0 Journal Article %D 2016 %T Quantum Merlin Arthur with Exponentially Small Gap %A Bill Fefferman %A Cedric Yen-Yu Lin %X We study the complexity of QMA proof systems with inverse exponentially small promise gap. We show that this class can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that a "precise" version of the Local Hamiltonian problem is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states is not as powerful as the ability to prepare the ground state of general Local Hamiltonians. %8 2016/01/08 %G eng %U http://arxiv.org/abs/1601.01975