Variational Rodeo Algorithm for Eigenstate Preparation

Preparing eigenstates of a system on a quantum computer is a non-trivial task. The Rodeo Algorithm (RA) has been shown to prepare eigenstates with high fidelity. A key feature of this algorithm is that excited states require no more work to prepare than ground states. However, its outcome is dependent on the ansatz having non-trivial overlap with the targeted state. We present the Variational Rodeo Algorithm (VRA), a variant of RA which uses variational methods to tune the ansatz. Thus, we avoid the limitations of RA while maximizing the probability of a successful run. Using Matrix Product States to perform a simulation of qubits, we show that the VRA is highly successful at preparing eigenstates with a fidelity which exceeds that of other variational methods as well as typical RA.