A solvable model of quantum random optimization problems

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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4 pages, 3 figures, accepted version

Scientific paper

10.1103/PhysRevLett.105.167204

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.

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