The complexity of the separable hamiltonian problem

André Chailloux, Or Sattath

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

In this paper, we study variants of the canonical Local Hamiltonian problem where, in addition, the witness is promised to be separable. We define two variants of the Local Hamiltonian problem. The input for the Separable Local Hamiltonian problem is the same as the Local Hamiltonian problem, i.e. a local Hamiltonian and two energies a and b, but the question is somewhat different: the answer is YES if there is a separable quantum state with energy at most a, and the answer is NO if all separable quantum states have energy at least b. The Separable Sparse Hamiltonian problem is defined similarly, but the Hamiltonian is not necessarily local, but rather sparse. We show that the Separable Sparse Hamiltonian problem is QMA(2)-Complete, while Separable Local Hamiltonian is in QMA. This should be compared to the Local Hamiltonian problem, and the Sparse Hamiltonian problem which are both QMA-Complete. To the best of our knowledge, Separable Sparse Hamiltonian is the first non-trivial problem shown to be QMA(2)-Complete.

Original languageEnglish
Title of host publicationProceedings - 2012 IEEE 27th Conference on Computational Complexity, CCC 2012
Pages32-41
Number of pages10
DOIs
StatePublished - 26 Sep 2012
Externally publishedYes
EventIEEE Computer Society Technical Committee on Mathematical Foundations of Computing - Porto, Portugal
Duration: 26 Jun 201229 Jun 2012

Conference

ConferenceIEEE Computer Society Technical Committee on Mathematical Foundations of Computing
Country/TerritoryPortugal
CityPorto
Period26/06/1229/06/12

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