Random quantum satisfiabiilty

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

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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
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
  • General Physics and Astronomy
  • Computational Theory and Mathematics


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


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