Fault-tolerant quantum computing in the Pauli or Clifford frame with slow error diagnostics

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. our scheme offers a few improvements over previously existing solutions, for instance it does not require active error correction and results in a reduced error-correction overhead when error diagnostics is much slower than the gate time. In addition, we adapt our protocol to cases where the underlying error correction strategy chooses the optimal correction amongst all Clifford gates instead of the usual Pauli gates. The resulting Clifford frame protocol is of independent interest as it can increase error thresholds and could find applications in other areas of quantum computation.