2026-07-22T08:34:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18324 2024-03-06T11:01:40Z ddc:004 open_access

Local Hamiltonians with No Low-Energy Stabilizer States Coble, Nolan J. Coudron, Matthew Nelson, Jon Nezhadi, Seyed Sajjad Hamiltonian complexity Stabilizer codes Low-energy states The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [Sevag Gharibian and François {Le Gall}, 2022] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [Anshu et al., 2022], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi 2023 Is Part Of LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2023.14 urn:nbn:de:0030-drops-183243 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.14 eng https://creativecommons.org/licenses/by/4.0/legalcode