Mitigating errors in logical qubits

Quantum error correcting codes can enable large quantum computations provided physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of exclusive decoders, which abort on decoding instances that are deemed too difficult. For the most discriminating of exclusive decoders, we demonstrate a threshold of 50% under depolarizing noise (or 32(1)% for the fault-tolerant case), and up to a quadratic improvement in logical failure rates below threshold. Furthermore, with a modest exclusion criterion, we identify a regime at low error rates where the exclusion rate decays with code distance, providing a pathway for scalable and time-efficient quantum computing with post-selection. Our exclusive decoder applied to magic state distillation yields a 75% reduction in the number of physical qubits, and a 60% reduction in the total spacetime volume, including accounting for repetitions. Other applications include error mitigation, and in concatenated schemes. Quantum error correction produces an enormous amount of data about the quantum system, including information about whether an uncorrectable error is likely. In this work the authors analyse a new decoder that can abort when decoding is deemed too difficult, yielding improved performance overall.