Scalable simultaneous multiqubit readout with $99.99\%$ single-shot fidelity

We describe single-shot readout of a trapped-ion multiqubit register using space- and time-resolved camera detection. For a single qubit we measure $0.9(3)\times {10}^{-4}$ readout error in $400$ $\mu$s exposure time, limited by the qubit’s decay lifetime. For a four-qubit register (a “qunybble”), we measure an additional error of only $0.1(1)\times {10}^{-4}$ per qubit, despite the presence of $4\%$ optical cross-talk between neighboring qubits. A study of the cross-talk indicates that the method would scale with a negligible loss of fidelity to $~$$10\hspace{0.5em}000$ qubits at a density of $\lesssim$$1$ qubit/$\mu$m${}^2$, with a readout time of $~1$ $\mu$s/qubit.

Figure 1

(a) ${}^{40}\mathrm{Ca}$${}^{+}$ levels. (b) Image cross-talk affecting ion 2 in a string of four ions. Inset: $50\times 10$ pixel acquisition area, at scale 2.6 $\mu$m/pixel. Filled circles show the integrated fluorescence from ion 2; the decreasing-brightness pixel order and data were obtained by averaging images in which only ion 2 was fluorescing. For the other three ions (open symbols), the same pixels were taken in the same order, but the data were taken from images in which only that ion was fluorescing. Up to $~$100 pixels, the region of interest (ROI) is roughly circular, centered on ion 2, with a diameter in the object plane given by the upper abscissa. The lines show calculated performance for a diffraction-limited imaging system of the same numerical aperture, with ion spacings 10 times smaller than in the image, on a $10\times$ magnified upper abscissa.

Figure 2

Single-ion readout results for space- and time-resolved detection. Analysis methods: (T)hreshold, (M)aximum likelihood, and (A)daptive maximum likelihood. (a) Integrated fluorescence signal and long-exposure image. (b) Single 400 $\mu$s exposure: readout error $\epsilon$ versus ROI size $N$. Inset: bright and dark photon count histograms for $N=30$, with threshold $\theta$. (c) Time-resolved detection using multiple 200 $\mu$s exposures with, above, example exposures 1–5 for bright- and dark-state preparation. Inset: minimum $\epsilon$ versus $N$ for method M.

Figure 3

Four-ion readout experiment. (a) Experimental sequence, showing a typical trial; maximum likelihood analysis applied to the 400 $\mu$s “test” exposure gives the qunybble state as {1110}, with estimated probability of error $\approx$${\sum }_{k=1}^4\hspace{0.5em}{\text{e}}^{-R_k}=1.4\times {10}^{-11}$. (b) Readout error per qubit averaged over trials of all 16 qunybble states $\{0000,\dots ,1111\}$, whose distribution is shown in the inset. The error due to $D$${}_{5/2}$ decay is excluded as described in the text. Analysis methods: (T)hreshold; (M)aximum likelihood ignoring neighbors; (MN) iterative maximum likelihood method taking into account nearest neighbors, with (solid line) a Monte Carlo simulation of ${10}^9$ trials. Adjacent ROIs overlap when their diameters exceed the 14 $\mu$m mean ion spacing.