A solvable model of quantum random optimization problems
arXiv:1006.1736 · doi:10.1103/PhysRevLett.105.167204
Abstract
We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems.
4 pages, 3 figures, accepted version