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2-Local Hamiltonian with Low Complexity is QCMA

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arxiv 1909.03787 v1 pith:PVYETCLJ submitted 2019-09-06 cs.CC quant-ph

Ying-hao Chen This is my paper · ORCID
classification cs.CCquant-ph
keywords complexityproblemqcmahamiltonianlocalargumentsbeencombining
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We prove that 2-Local Hamiltonian (2-LH) with Low Complexity problem is QCMA-complete by combining the results from the QMA-completeness[4] of 2-LH and QCMA-completeness of 3-LH with Low Complexity[6]. The idea is straightforward. It has been known that 2-LH is QMA-complete. By putting a low complexity constraint on the input state, we make the problem QCMA. Finally, we use similar arguments as in [4] to show that all QCMA problems can be reduced to our proposed problem.

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Cited by 1 Pith paper

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  1. Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes

    quant-ph 2025-06 conditional novelty 8.0 of 10

    New QSAT variants on qubits and qudits are complete for BQP_1, coRP, QCMA and six PI/SoPU classes, implying any classification of strong quantum CSPs must contain at least 13 classes unless some collapse.

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