The feed-forward latency requirements for Quantum Error Correction

One of the greatest challenges in performing fault-tolerant quantum computing in quantum error correction (QEC) is reaching low feed-forward latencies, that is, a short time from the physical execution of a logical measurement until the controller plays a conditional pulse which depends on the logical measurement outcome. The necessity for feed-forward arises from the requirement to perform non-Clifford gates to reach quantum advantage (Gottesman-Knill theorem). To keep track of the logical flips and correct them without propagation, the conditional feed-forward of each non-Clifford gate must depend on the decoding. Here, we provide a general analysis of the feed-forward latency requirements with the latency behavior in different classical setups. Using a dynamical system analysis we show the conditions on the system latency performance that determine the operation regime: latency divergence, where quantum calculations are unfeasible, classical-controller limited runtime, or quantum-operation limited runtime where the classical operations do not delay the quantum circuit. The proposed analysis can be used for any decoding algorithm and any QEC stabilizer code towards fault-tolerant quantum computation.