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arXiv · 2509.25821

On the Complexity of the Succinct State Local Hamiltonian Problem

Gabriel Waite·Karl Lin
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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 2-Local Hamiltonian problem, for qubit Hamiltonians, is (promise) MA-complete. The approach combines a systematic characterisation of succinct quantum states, defined through arithmetic over specific number fields, with a refined reduction that lowers the locality of Feynman-Kitaev circuit-Hamiltonians from 6 to 2, without increasing particle dimension. This reveals a complexity phase transition, parameterised by locality, and extends the scope of previously known MA-complete problem instances. Our results further clarify how succinctness behaves under circuit-based constructions, and progresses toward a better understanding of the boundary between efficiently describable and efficiently verifiable quantum systems.

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Gabriel Waite, Karl Lin. 2025-09-30. On the Complexity of the Succinct State Local Hamiltonian Problem. https://arxiv.org/abs/2509.25821

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