Quantum sensing with tunable superconducting qubits: optimization and speed-up

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.