2026-07-21T03:15:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24061 2025-12-12T14:56:13Z ddc:004 open_access

The Rotation-Invariant Hamiltonian Problem Is QMA_EXP-Complete Nelson, Jon Gottesman, Daniel Hamiltonian complexity Local Hamiltonian problem Monogamy of entanglement In this work we study a variant of the local Hamiltonian problem where we restrict to Hamiltonians that live on a lattice and are invariant under translations and rotations of the lattice. In the one-dimensional case this problem is known to be QMA_EXP-complete. On the other hand, if we fix the lattice length then in the high-dimensional limit the ground state becomes unentangled due to arguments from mean-field theory. We take steps towards understanding this complexity spectrum by studying a problem that is intermediate between these two extremes. Namely, we consider the regime where the lattice dimension is arbitrary but fixed and the lattice length is scaled. We prove that this rotation-invariant Hamiltonian problem is QMA_EXP-complete answering an open question of [Gottesman and Irani, 2013]. This characterizes a broad parameter range in which these rotation-invariant Hamiltonians have high computational complexity. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jon Nelson and Daniel Gottesman 2025 Is Part Of LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2025.12 urn:nbn:de:0030-drops-240615 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.12 eng https://creativecommons.org/licenses/by/4.0/legalcode