Rodeo Algorithm for Quantum Computing

Understand

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$.

• In order to reduce the spectral weight of all other eigenvectors by a suppression factor $\delta$, the required computational effort scales as $O[|\log \delta|/(p \epsilon)]$, 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 $E$.
• With each auxiliary qubit measurement, the amplitudes of the eigenvectors are multiplied by a stochastic factor that depends on the proximity of their energy to $E$.