  Subsystem readout during a quantum process, or mid-circuit measurement, is
crucial for error correction in quantum computation, simulation, and metrology.
Ideal mid-circuit measurement should be faster than the decoherence of the
system, high-fidelity, and nondestructive to the unmeasured qubits. Here, we
use a strongly coupled optical cavity to read out the state of a single
tweezer-trapped 87Rb atom within a small tweezer array. Measuring either atomic
fluorescence or the transmission of light through the cavity, we detect both
the presence and the state of an atom in the tweezer, within only tens of
microseconds, with state preparation and measurement infidelities of roughly
0.5% and atom loss probabilities of around 1%. Using a two-tweezer system, we
find measurement on one atom within the cavity causes no observable
hyperfine-state decoherence on a second atom located tens of microns from the
cavity volume. This high-fidelity mid-circuit readout method is a substantial
step towards quantum error correction in neutral atom arrays.
