PIRSA:09120031

Random quantum satisfiability: statistical mechanics of quantum optimization

Laumann, C. (2009). Random quantum satisfiability: statistical mechanics of quantum optimization. Perimeter Institute. https://pirsa.org/09120031

Laumann, Christopher. Random quantum satisfiability: statistical mechanics of quantum optimization. Perimeter Institute, Dec. 14, 2009, https://pirsa.org/09120031 

          @misc{ pirsa_PIRSA:09120031,
            doi = {10.48660/09120031},
            url = {https://pirsa.org/09120031},
            author = {Laumann, Christopher},
            keywords = {Quantum Information},
            language = {en},
            title = {Random quantum satisfiability: statistical mechanics of quantum optimization},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {dec},
            note = {PIRSA:09120031 see, \url{https://pirsa.org}}
          }

Chris Laumann

Boston University

Talk number
PIRSA:09120031
Collection
Talk Type
Subject
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. Inspired by the success of the statistical study of classical constraint optimization problems, we study random ensembles of the QMA$_1$-complete quantum satisfiability (QSAT) problem introduced by Bravyi. 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 product satisfiable, entangled satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for a fixed interaction graph exhibit the same dimension of the satisfying manifold. This establishes the generic QSAT decision problem as equivalent to a purely graph theoretic property and that the hardest typical instances are likely to be localized in a bounded range of clause density. Based on papers: C.R. Laumann, R. Moessner, A. Scardicchio, and S.L. Sondhi. Phase transitions and random quantum satisfiability. QIC 10 (1/2), (2009). arXiv:0903.1904 C.R. Laumann, A.M. Lauchli, R. Moessner, A. Scardicchio, and S.L. Sondhi. On product, generic and random generic quantum satisfiability. arXiv:0910.2058