Abstract The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising
variational quantum algorithm that aims to solve combinatorial optimization problems that …

In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

The problem of optimizing over random structures emerges in many areas of science and
engineering, ranging from statistical physics to machine learning and artificial intelligence …

Let A∈\mathbbR^n*n be a symmetric random matrix with independent and identically
distributed (iid) Gaussian entries above the diagonal. We consider the problem of …

Approximate Message Passing algorithms for rotationally invariant matrices Page 1 The
Annals of Statistics 2022, Vol. 50, No. 1, 197–224 https://doi.org/10.1214/21-AOS2101 © …

Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge
in many areas of science. Some intriguing and not fully understood examples are the glassy …

We study the problem of algorithmically optimizing the Hamiltonian HN H_N of a spherical or
Ising mixed pp‐spin glass. The maximum asymptotic value OPT OPT of HN/N H_N/N is …

We consider the problem of finding nearly optimal solutions of optimization problems with
random objective functions. Such problems arise widely in the theory of random graphs …

Let Φ be a uniformly random k-SAT formula with n variables and m clauses. We study the
algorithmic task of finding a satisfying assignment of Φ. It is known that satisfying …

The Quantum Approximate Optimization Algorithm (QAOA) is a general purpose quantum
algorithm designed for combinatorial optimization. We analyze its expected performance …