Rodeo Algorithm for Quantum Computing.

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval [E-ε,E+ε]. In order to reduce the spectral weight of all other eigenvectors by a suppression factor δ, the required computational effort scales as O[|logδ|/(pε)], where p is the squared overlap of the initial state with the target eigenvector. The method, which we call the rodeo algorithm, uses auxiliary qubits to control the time evolution of the Hamiltonian minus some tunable parameter E.