  Scaling up invariably error-prone quantum processors is a formidable
challenge. While quantum error correction ultimately promises fault-tolerant
operation, the required qubit overhead and error thresholds are daunting, and
many codes break down under correlated noise. Recent proposals have suggested a
complementary approach based on co-located, auxiliary 'spectator' qubits. These
act as in-situ probes of noise, and enable real-time, coherent corrections of
the resulting errors on the data qubits. Here, we use an array of cesium
spectator qubits to correct correlated phase errors on an array of rubidium
data qubits. Crucially, by combining in-sequence readouts, data processing, and
feed-forward operations, these correlated errors are suppressed within the
execution of the quantum circuit. The protocol is broadly applicable to quantum
information platforms, and our approach establishes key tools for scaling
neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time
processing and feed-forward, and coherent mid-circuit reloading of atomic
qubits.
