Abstract 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 Ceramic Terminal Strip 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 Blood Pressure Kits 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.