I was reading the paper about "Cleaner magic states with hook injection"1, which is really cool, and I get technically, but it is unclear in which stages do you perform the post-selection.
Alternatively, which measurements along the way would cause discarding the process?
This is explained in figure 2 of the paper. In that figure, every measurement with a teal outline has a predictable value. If any of them report a different value from what's expected, all the qubits are cleared and the injection process restarts. The restart is assumed to occur immediately after the second round finishes.
In practice there would be some delay from the control system making the discard decision by checking the measurements. So maybe there would be a holding-pattern round to give it time to do that. Also in practice if you saw the first layer of measurements fail, you would probably restart right away instead of continuing with the second round.
Here's the figure:
In the first round, only measurements whose stabilizer matched the initialization basis can be predicted:
In the second round, all measurements can be predicted:
The postselection is performed in simulation by giving the --postselected_detectors_predicate argument to sinter collect. It doesn't bother with restart logic, it just runs the whole circuit including the stuff after the injection and throws away any shots where any of the specified postselected detectors fired.
