Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

We review here some recent work in the field of quantum annealing, alias adiabatic
quantum computation. The idea of quantum annealing is to perform optimization by a …

We study the satisfiability of randomly generated formulas formed by M clauses of exactly K
literals over N Boolean variables. For a given value of N the problem is known to be most …

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 …

Heuristic methods are used when rigorous ones are either unknown or cannot be applied,
typically because they would be too slow. A metaheuristic is a general optimization …

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean
variables. Using the cavity method at zero temperature, we find the phase diagram for the K …

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 …

Using the cavity equations of Mézard, Parisi, and Zecchina Science 297 (2002), 812;
Mézard and Zecchina, Phys Rev E 66 (2002), 056126 we derive the various threshold …

Boolean satisfiability (k-SAT) is one of the most studied optimization problems, as an
efficient (that is, polynomial-time) solution to k-SAT (for k≥ 3) implies efficient solutions to a …

Using elementary rigorous methods we prove the existence of a clustered phase in the
random K-SAT problem, for K≥ 8. In this phase the solutions are grouped into clusters …