Fault-tolerant quantum metrology

We show how fault-tolerant quantum metrology can overcome noise beyond our control -- associated with sensing the parameter, as well as under our control -- in preparing and measuring probes and ancillae. To that end, we introduce noise thresholds to quantify the noise resilience of parameter estimation schemes. We demonstrate improved noise thresholds over the non-fault tolerant schemes. We use quantum Reed-Muller codes to retrieve more information about a single phase parameter being estimated in the presence of full-rank Pauli noise. Further improvements in fault-tolerant quantum metrology could be achieved by optimising in tandem parameter-specific estimation schemes and transversal quantum error correcting codes.