Real-time decoding of repeated stabilizer measurements in a bit-flip code

Although qubit coherences and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation is necessary to implement a universal gate set without delaying the processor. Here we present a classical control architecture for the fast extraction of errors based on multiple rounds of stabilizer measurements, and subsequent optional correction. We demonstrate its application on a minimal bitflip code with five transmon qubits, showing that error tracking based on multiple stabilizer rounds is superior to round-by-round correction, while introducing minimal latency. This co-processing of classical and quantum information will be crucial in running a logical circuit at its full speed to outpace error accumulation.