We construct a pairwise measurement-based code on eight qubits that is error-correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest-neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28. We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group. We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement. We estimate the pseudothreshold to be between ${10}^{-5}$ and $2\times {10}^{-4}$, depending on the amount of noise on idle physical qubits. The use of postselection in addition to error correction (correcting all degree-one faults and rejecting a subset of the higher degree faults) can improve the pseudothreshold by up to an order of magnitude.

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• Quantum error correction