Quantum computation based on resonance transition

We present an approach for quantum computation based on resonance transition (QCRT). In the QCRT approach, any eigenstate of an arbitrary Hamiltonian can be obtained through a resonance mechanism combined with partial measurements. We found that for a Hamiltonian whose ground state encodes the solution to a problem, if it has the structure that the ratio between the degeneracies of any two energy levels is polynomial large, then the problem can be solved in polynomial time using the QCRT approach. Based on this fi nding, we have applied the QCRT approach for obtaining energy spectrum and eigenstates of a physical system, factoring large integers, and for solving the search problem, the 3-bit exact cover problem and the optimization problem. A quantum cooling algorithm is also proposed based on the QCRT approach.