Impact of Decoding Latency in the Assessment of Quantum Surface Codes Performance

To advance the field of quantum computing, quantum error correction codes are essential to preserve and elaborate quantum information. Among the various candidates for near-term quantum error correction, surface codes stand out due to their structure and the availability of efficient decoding strategies. Performance assessments of these codes have been focused mainly on the qubit error probability, overlooking the impact of decoherence over time when decoders with different latencies are employed. In this paper, we present a simple framework to address this limitation, deriving performance metrics that incorporate the time complexity of the decoding process.