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
Volume5125 LNCS
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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Hamiltonians
Qubit
Workspace
Interaction
Triangle
Verify
Three-dimensional

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

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., Vol. 5125 LNCS, 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

Quantum SAT for a qutrit-cinquit pair is QMA1-complete. / Eldar, Lior; Regev, Oded.

Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings. Vol. 5125 LNCS PART 1. ed. Springer Verlag, 2008. p. 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).

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

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 edn, vol. 5125 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 5125 LNCS, Springer Verlag, pp. 881-892, 35th International Colloquium on Automata, Languages and Programming, ICALP 2008, Reykjavik, Iceland, 7/7/08. https://doi.org/10.1007/978-3-540-70575-8_72
Eldar L, Regev O. Quantum SAT for a qutrit-cinquit pair is QMA1-complete. In Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings. PART 1 ed. Vol. 5125 LNCS. Springer Verlag. 2008. p. 881-892. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-540-70575-8_72
Eldar, Lior ; Regev, Oded. / Quantum SAT for a qutrit-cinquit pair is QMA1-complete. Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings. Vol. 5125 LNCS PART 1. ed. Springer Verlag, 2008. pp. 881-892 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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