Efficient Characterization of a Unitary Quantum Gate via a Projective Rabi Experiment

Abstract

In this thesis, we introduce a novel randomization-based protocol for estimation of parameters in a sparse Hamiltonian. This is achieved via a projective Rabi experiment which interleaves projective channels between applications of a fixed quantum channel of interest to allow for a coherent amplification of some small user selectable subspace. An important result that we prove is the efficiency and robustness of the protocol making it a suitable for experimental systems. Specifically, we prove it is Heisenberg-limited meaning the uncertainty in the output reaches the best case scaling with experimental time restricted only by the fundamental limit of quantum physics. For this thesis, we outline the abstract algorithm and demonstrate how to construct approximate projectors using the character projection formula. Then, we prove the efficiency and robustness of the protocol. Finally, we walk through an example of a multi-qudit rotation gate demonstrating the functionality of our methodology and run numerical simulations to validate our results.