Fig. 5: Performance of quantum-frequency discrimination as a function of available resources for \(\omega _1 = (2\pi ) \cdot 0.999\) MHz, \(\omega _2 = (2\pi ) \cdot 1.001\) MHz.

a Experimental frequency discrimination error as a function of coherent interaction time. Data points are for sensor readout using a single SSR measurement (orange, N_RR = 10⁴) and ensemble averaging (lilac, N_ens = 10⁴). Fits are from Supplementary Eq. 89 and 91. The ideal SSR curve corresponds to perfect sensor initialization and mapping to ancilla. b Experimental frequency discrimination error as a function of detected photons for a single SSR measurement (orange) and ensemble averaging (lilac), for an interaction time of 44 µs \(\left( {\varphi _{\Delta} = \pi } \right)\). Imperfect sensor initialization limits the error achievable with a single SSR measurement. c Frequency discrimination error as a function of total measurement time for a single SSR measurement (orange, N_RR = 10⁴) and ensemble averaging (lilac, N_ens = 10⁴). Each data point corresponds to a different interaction time. d Frequency discrimination error as a function of total measurement time, with a fixed interaction time of 44 µs \(\left( {\varphi _{\Delta} = \pi } \right)\). Although for SSR (orange) the total time is incremented by performing additional measurements (each using N_RR = 10⁴), for ensemble averaging N_ens is increased. Expected errors obtained from simulations for \(N_{{\mathrm{RR}}} = 10^2,\;10^3,\;10^4\) are included (solid blue, green, and yellow lines, see Supplementary Note 4). e Frequency discrimination error as a function of number of trials, i.e., number of times the signal is interrogated, with a fixed interaction time of 44 µs using many SSR (each using N_RR = 10⁴, orange) or ensemble averaging (lilac). Error bars are 1 SD.