A quantum algorithm for solving some discrete mathematical problems by   probing their energy spectra
  When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems. 
Hefeng Wang, Heng Fan and Fuli Li
quant-ph