Simulation of exceptional-point systems on quantum computers for quantum sensing

Abstract: There has been debate around applicability of exceptional points (EP) for quantum sensing. To resolve this, we first explore how to experimentally implement the nonhermitian non-diagonalizable Hamiltonians, that exhibit EPs, in quantum computers which run on unitary gates. We propose to use an ancilla-based method in this regard. Next, we show how such Hamiltonians can be used for parameter estimation using quantum computers and analyze its performance in terms of the Quantum Fisher Information ($QFI$) at EPs, both without noise and in presence of noise. It is well known that $QFI$ of a parameter to be estimated is inversely related to the variance of the parameter by the quantum Cramer-Rao bound. Therefore the divergence of the $QFI$ at EPs promise sensing advantages. We experimentally demonstrate in a cloud quantum architecture and theoretically show, using Puiseux series, that the $QFI$ indeed diverges in such EP systems which were earlier considered to be non-divergent.