Quantum Fourier transform for nanoscale quantum sensing

The Quantum Fourier Transformation ($QFT$) is a key building block for whole wealth of quantum algorithms. Despite its proven efficiency, only few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance the performance sensor. We implement algorithm in hybrid register consisting nitrogen-vacancy (NV) center electron spin and three nuclear spins. runs on spins serves process sensor - NV signal. demonstrate (spins) classical signals (radio frequency (RF) ) with near Heisenberg limited precision scaling. further show application demultiplexing magnetic resonance (NMR) signal two distinct target Our results mark complex sensing which particular interest high dynamic range nanoscale NMR spectroscopy experiments.