Average execution time for T gate

In the surface code there are two major costs to T gates: the spacetime cost and the reaction time cost.

The spacetime cost is due to the need to perform magic state distillation of a T state for each T gate, which takes hundreds of operations. A T gate factory producing a T state every hundred microseconds can easily monopolize a hundred thousand qubits. This isn't technically a limitation on the time of the computation, because you can just add more and more factories until the T gates are coming at any rate you want, but it represents a large cost that forces hard tradeoffs between more space usage and longer runtime. See https://arxiv.org/abs/1812.01238 and https://arxiv.org/abs/1905.06903. For scale:

The reaction time cost has to do with the fact that when you teleport through a T gate, you instead apply its inverse 50% of the time. You realize that it happened, but it still has to be fixed before the computation can properly progress. Ultimately this means that if you have a series of T gates to apply, you are limited by how fast you can figure out if you did T or inverse T and then correct it. In fact this is the only part of a quantum computation that isn't embarrassingly parallel. There is a technique where this time is minimized by preparing a wordline for each possible correction, and teleporting through the one that matters. With that technique the T depth of your circuit times your control system's reaction time is a lower bound on how fast the computation can finish. See https://arxiv.org/abs/1210.4626 and https://arxiv.org/abs/1905.08916.