Extended Data Fig. 3: Mid-circuit readout and feedforward.

a, Single-shot 500-μs local image in the readout zone, in which the peak corresponds to roughly 50 photons collected by the CMOS camera. b, Atomic transition and pulse sequence used for local imaging of ancilla qubits. The data-qubit trap-light shift suppresses data qubit errors, as well as the large spatial separation between entangling and readout zones. We avoid quickly losing the readout-zone atoms during local imaging by using a 5× higher trap depth and we pulse the ancilla qubit traps and local imaging light to image directly on resonance while avoiding negative effects of large trap-light shifts. c, Diagram of components involved in mid-circuit readout and feedforward steps. Atom detection and logical-state decoding occur using the FPGA, which then outputs a conditional TTL to gate local Raman pulses performed on logical qubits in the entangling zone. d, Diagram of approximate timings for a mid-circuit feedforward cycle. First, the F = 2 population is pushed out (in 10 μs) and then the remaining F = 1 population is imaged locally for 500 μs. The 24 rows of pixels covering the readout zone are read out to the FPGA in 200 μs, after which processing is performed. Finally, a conditional TTL output based on the decoded state gates on or off local Raman pulses. The whole readout and feedforward cycle takes less than 1 ms and can be sped up in the future by optimizing local imaging and camera readout. e–g, Characterization of the error probability of data qubits during local imaging. e, Data-qubit error probability (fraction of population depumped from F = 2 to F = 1) as a function of local imaging duration out to 20 ms to quantify the effect of the local imaging beam on data-qubit coherence for very long illumination. f, Data-qubit error probability after 20 ms of local imaging, as a function of detuning of the local imaging beam, showing suppression of error red-detuned or blue-detuned from the data-qubit transition. g, Equivalently, increasing the trap depth of the data qubits enables suppression of decoherence owing to the local imaging beam. Because qubits in the readout zone are imaged while their traps are pulsed off, any light shift of the data-qubit transition from the traps contributes directly to the relative detuning. h, For a long, 10.5-ms local beam illumination with optimal local imaging parameters, we observe a 0.7(1)% increase in data-qubit error during an XY8 dynamical decoupling sequence. This suggests a roughly 0.034(5)% error probability for the data qubits during the 500-μs mid-circuit readout image used in this work.