On the Complexity of the Succinct State Local Hamiltonian Problem

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.