A quantum algorithm to produce any eigenstate of any unitary without measurement

Unitary evolutions underpin all of noiseless quantum computing. Often, the eigenstates of a unitary evolution are unknown but are required for a larger computation. Current techniques for producing these eigenstates involve computationally expensive full-state tomography and costly circuit design to produce the eigenstates. In this talk, I present a simplistic algorithm for coherently producing any eigenstate without measurement. By generalizing the quantum-amplitude-estimation algorithm such that it does not require an oracle, we show that is possible to amplify any initial state with non-zero overlap with any target eigenstate of an unknown unitary. We apply our algorithm to a d-dimension oscillator system and demonstrate, analytically and numerically, that our algorithm can produce the ground state. We also show that our algorithm can be applied to unstructured search problems.