JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR SPECIAL SEMINAR: Phase transitions and random quantum satisfiability
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 satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for any hypergraph exhibit the same
dimension of the satisfying manifold. This establishes the random 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.
Work done in collaboration with R. Moessner, A. Scardicchio and S. Sondhi.
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