Among various algorithms designed to exploit the specific properties of quantum computers
with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to …

We establish the satisfiability threshold for random k-SAT for all k≥ k0. That is, there exists a
limiting density αs (k) such that a random k-SAT formula of clause density α is with high …

For a number of random constraint satisfaction problems, such as random k-SAT and
random graph/hypergraph coloring, there are very good estimates of the largest constraint …

Physics-based Ising machines (IM) have been developed as dedicated processors for
solving hard combinatorial optimization problems with higher speed and better energy …

Discrete combinatorial optimization has a central role in many scientific disciplines,
however, for hard problems we lack linear time algorithms that would allow us to solve very …

We consider the random regular k-nae-sat problem with n variables each appearing in
exactly d clauses. For all k exceeding an absolute constant k 0, we establish explicitly the …

We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising
model on general graphs. We show that if (d-1)\tanhβ<1, then there exists a constant C such …

Constraint satisfaction problems are ubiquitous in many domains. They are typically solved
using conventional digital computing architectures that do not reflect the distributed nature of …

We introduce a novel entropy-driven Monte Carlo (EdMC) strategy to efficiently sample
solutions of random constraint satisfaction problems (CSPs). First, we extend a recent result …

Optimizing highly complex cost/energy functions over discrete variables is at the heart of
many open problems across different scientific disciplines and industries. A major obstacle …