Statistical approach to quantum phase estimation

We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike traditional iterative PEAs which return only an eigenphase estimate, proposed method can determine any unknown eigenstate-eigenphase pair from given unitary matrix utilizing simplified version of hardware intended for Iterative PEA (IPEA). This is achieved by treating probabilistic output IPEA-like circuit as proximity metric, using this metric estimate input state nearest approaching via process on phase. may search over entire computational space, or efficiently eigenphases (eigenstates) within some specified range (directions), allowing those with prior knowledge their system particular solutions. show simulation results Qiskit package IBM Q platform local computer.