On the Complexity of the Succinct State Local Hamiltonian Problem

Abstract: We study the computational complexity of the Local Hamiltonian problem under the promise that its ground state is succinctly represented. We show that the Succinct State 3-Local Hamiltonian problem is (promise) MA-complete. Our proof proceeds by systematically characterising succinct quantum states and modifying the original MA-hardness reduction. In particular, we show that a broader class of succinct states suffices to capture the hardness of the problem, extending and strengthening prior results to classes of Hamiltonians with lower locality.