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Although qubit coherence times 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 adding significant delays in the processor. Here we realize a classical control architecture for the fast extraction of errors based on multiple cycles of stabilizer measurements and subsequent correction. We demonstrate its application on a minimal bit-flip code with five transmon qubits, showing that real-time decoding and correction based on multiple stabilizers is superior in both speed and fidelity to repeated correction based on individual cycles. Furthermore, the encoded qubit can be rapidly measured, thus enabling conditional operations that rely on feed-forward, such as logical gates. This co-processing of classical and quantum information will be crucial in running a logical circuit at its full speed to outpace error accumulation.
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the smallest QEC
Real stabilizer operators, which are also known as real Clifford operators, are generated, through composition and tensor product, by the Hadamard gate, the Pauli Z gate, and the controlled-Z gate. We introduce a normal form for real stabilizer circu
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the codes maximum stabilizer generator weight. For some common distance-three codes, the recent flag paradigm uses just two extra q
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the successful perfo
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near