  Sensing and metrology play an important role in fundamental science and
applications by fulfilling the ever-present need for more precise data sets and
by allowing researchers to make more reliable conclusions on the validity of
theoretical models. Sensors are ubiquitous. They are used in applications
across a diverse range of fields including gravity imaging, geology,
navigation, security, timekeeping, spectroscopy, chemistry, magnetometry,
healthcare, and medicine. Current progress in quantum technologies has
inevitably triggered the exploration of the use of quantum systems as sensors
with new and improved capabilities. This article describes the optimization of
the quantum-enhanced sensing of external magnetic fluxes with a Kitaev phase
estimation algorithm based on a sensor with tunable transmon qubits. It
provides the optimal flux biasing point for sensors with different maximal
qubit transition frequencies. An estimation of decoherence rates is made for a
given design. The use of $2-$ and $3-$qubit entangled states for sensing are
compared in simulation with the single qubit case. The flux sensing accuracy
reaches $10^{-8}\cdot\Phi_0$ and scales with time as $\sim\ 1/t$ which proves
the speed-up of sensing with high ultimate accuracy.
