Quoting Orion from Cirq Sync:

@daxfohl is doing "something" with act on args to make it cleaner and this looks related to his stuff.

I removed everywhere where the gates had special simulator-specific handling in their act_on implementation, basically establishing a convention that simulators were a layer on top of gates, not vice-versa. This was mostly done in #4748.

However IIUC these gates are targeted specifically to the Tableau sampler, and not be used as general-purpose gates. So it makes sense here to allow these gates to reference the Tableau directly in their act_on implementation. In fact it's a great example of when this pattern can be used, to create a special gate type specific to a simulator, without having to modify the simulator code itself.

The alternative would be to add some abstract get_custom_strategies() in act_on_stabilizer_args and append the results of that here. https://github.com/quantumlib/Cirq/blob/master/cirq-core/cirq/sim/clifford/act_on_stabilizer_args.py#L94. The default implementation would return an empty list, and the tableau implementation could return a strategy that handles SingleQubitCliffordGates.

That said, it seems like overkill and I think the act_on implementation is cleaner.

@BichengYing is something like https://github.com/quantumlib/Cirq/compare/main...daxfohl:clifford-acton?expand=1 what you're looking for? If so, I can open a PR.