Cavity-Coupled Neutral Atom Array Part 2: Classical Error Correction of a 5-Bit Atomic Register

We present further capabilities of our system, an optical cavity integrated with an atom array, in speeding up array readout and performing classical error correction. To speed up array readout, we use adaptive search strategies which utilize global/subset checks in lieu of strictly sequential readout. In our finitely sized system where the atoms are biased to be in the dark state, the array readout is often complete after an initial global check. As a step toward fault tolerance, we also demonstrate repeated rounds of classical error correction on a register of atomic bits. We encode a logical bit into the hyperfine state of multiple atoms and introduce bit flip errors on each atom with a fixed probability. Using sequential measurements of each atom and a majority vote to determine the logical state of the register, we measure and correct the register for up to 17 rounds. We see exponential suppression of logical error and extension of the logical memory fivefold beyond the single-bit idling lifetime. These results demonstrate key capabilities for scalable measurement-based protocols and quantum error correction.