Fault-Tolerant Quantum Metrology with High-Density Spin Ensembles: Theory

One of the most promising routes towards high-sensitivity quantum metrology is to utilize high density spin ensembles. Here, spins are typically periodically manipulated in order to both extend coherence and detect an external signal at a particular frequency. However, spin-spin interactions and on-site disorder may severely limit the coherence time and the achievable sensitivities under such dynamical protocols. In addition, control imperfections pose a significant challenge to the effectiveness of decoupling and sensing sequences. Here, we present a novel formalism for the fault-tolerant design of sensing sequences that simultaneously decouples interactions and suppresses the effects of disorder and imperfect controls, while maximizing sensitivity to an external signal. In addition to the broad applicability to different decoupling and sensing scenarios, this formalism could also serve as a powerful tool for the engineering of Hamiltonians to study many-body physics.