Site-Selective Cavity Readout and Classical Error Correction of a 5-Bit Atomic Register

Optical cavities can provide fast and nondestructive readout of individual atomic qubits; however, scaling up to many qubits remains a challenge. Using locally addressed excited-state Stark shifts to tune atoms out of resonance, we realize site-selective hyperfine-state cavity readout across a ten-site array. The state discrimination fidelity is 0.994(1) for one atom and 0.989(2) averaged over the entire array at a survival probability of 0.975(1). To further speed up array readout, we demonstrate adaptive search strategies utilizing global or subset checks. Finally, we demonstrate repeated rounds of classical error correction, showing exponential suppression of logical error and extending logical memory fivefold beyond the single-bit idling lifetime.