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 …

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 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 consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

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 …

Note: This Perspective offers a progress report for the Simons collaboration “Cracking the
Glass Problem,” of which the authors are some of the principal investigators. While the …

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 …

We discuss an analysis of constraint satisfaction problems, such as sphere packing, K-SAT,
and graph coloring, in terms of an effective energy landscape. Several intriguing geometrical …

The path integral Monte Carlo simulated quantum annealing algorithm is applied to the
optimization of a large hard instance of the random satisfiability problem (N= 10 000). The …

We propose a modified belief propagation algorithm, with over-relaxed dynamics. Such an
algorithm turns out to be generally more stable and faster than ordinary belief propagation …