Quantum SAT for a qutrit-cinquit pair is QMA1-complete

Lior Eldar, Oded Regev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We show that the quantum SAT problem is QMA1-complete when restricted to interactions between a three-dimensional particle and a five-dimensional particle. The best previously known result is for particles of dimensions 4 and 9. The main novel ingredient of our proof is a certain Hamiltonian construction named the Triangle Hamiltonian. It allows to verify the application of a 2-qubit CNOT gate without generating explicitly interactions between pairs of workspace qubits. We believe this construction may contribute to progress in other Hamiltonian-related problems as well as in adiabatic computation.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
PublisherSpringer Verlag
Pages881-892
Number of pages12
EditionPART 1
ISBN (Print)3540705740, 9783540705741
DOIs
StatePublished - 2008
Event35th International Colloquium on Automata, Languages and Programming, ICALP 2008 - Reykjavik, Iceland
Duration: Jul 7 2008Jul 11 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other35th International Colloquium on Automata, Languages and Programming, ICALP 2008
CountryIceland
CityReykjavik
Period7/7/087/11/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Eldar, L., & Regev, O. (2008). Quantum SAT for a qutrit-cinquit pair is QMA1-complete. In Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings (PART 1 ed., pp. 881-892). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5125 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-540-70575-8_72