Fault-tolerant quantum metrology

Abstract: We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with 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. Using only error detection, as opposed to error correction, allows us to retrieve higher thresholds. We show that better devices, which can be engineered, can enable us to counter larger noise in the field beyond our control. Further improvements in fault-tolerant quantum metrology could be achieved by optimising in tandem parameter-specific estimation schemes and transversal quantum error correcting codes.