A quantum algorithm for obtaining the energy spectrum of a physical system without guessing its eigenstates

We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register $R$ which consists of one ancilla qubit and a $n$-qubit register that represents the system. $R$ is prepared in a general reference state, and a general excitation operator acts on $R$ is constructed. The probe exhibits a dynamical response only when it is resonant with a transition from the reference state to an excited state of $R$ which contains the eigenstates of the system. By varying the probe's frequency, the energy spectrum and the eigenstates of the system can be obtained.

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