Random quantum satisfiabiilty

C. R. Laumann, R. Moessner, A. Scardicchio, Shivaji Lal Sondhi

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA1-complete quantum satisfiability (QSAT) problem introduced by Bravyi [1]. QSAT appropriately generalizes the NP-complete classical satisfiability (SAT) problem. We show that, as the density of clauses/projectors is varied, the ensembles exhibit quantum phase transitions between phases that are satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for any hypergraph exhibit the same dimension of the satisfying manifold. This establishes the QSAT decision problem as equivalent to a, potentially new, graph theoretic problem and that the hardest typical instances are likely to be localized in a bounded range of clause density.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalQuantum Information and Computation
Volume10
Issue number1-2
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Computational Theory and Mathematics

Keywords

  • Average case complexity
  • Disordered quantum satisfiability
  • QSAT
  • SAT

Fingerprint Dive into the research topics of 'Random quantum satisfiabiilty'. Together they form a unique fingerprint.

  • Cite this

    Laumann, C. R., Moessner, R., Scardicchio, A., & Sondhi, S. L. (2010). Random quantum satisfiabiilty. Quantum Information and Computation, 10(1-2), 1-15.