  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.
