2026-08-10T22:48:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5846 2024-03-06T10:37:12Z ddc:004 open_access

Complexity Classification of Two-Qubit Commuting Hamiltonians Bouland, Adam Mancinska, Laura Zhang, Xue Quantum Computing Sampling Problems Commuting Hamiltonians IQP Gate Classification Theorems We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one to sample from probability distributions which cannot be sampled from classically unless the polynomial hierarchy collapses. Furthermore, the only simulable Hamiltonians are those which fail to generate entanglement. This shows that generic two-qubit commuting Hamiltonians can be used to perform computational tasks which are intractable for classical computers under plausible assumptions. Our proof makes use of new postselection gadgets and Lie theory. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Adam Bouland and Laura Mancinska and Xue Zhang 2016 Is Part Of LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2016.28 urn:nbn:de:0030-drops-58469 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.28 eng https://creativecommons.org/licenses/by/3.0/legalcode