00861nas a2200121 4500008004100000245005500041210005500096260001500151520049300166100002000659700002400679856003600703 2016 eng d00aQuantum Merlin Arthur with Exponentially Small Gap0 aQuantum Merlin Arthur with Exponentially Small Gap c2016/01/083 aWe 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.1 aFefferman, Bill1 aLin, Cedric, Yen-Yu uhttp://arxiv.org/abs/1601.01975