as mentioned turbo charging a 2 stroke is not a simple task, even with a disk valved engine its a whole new world of tuning.
this is the engine from the current 50cc world record holder. its a Kreidler, and its turbo charged.
however it is possible to run a piston ported 2 stroke on boost, it does however get extremely complicated. i talked to a guy once who ran a snow mobile set up like this and just listening to him try to explain it made my head want to explode.
you basically have to run a specially designed expansion chamber, for starters, one that will create a great amount of back pressure and very low amount of flow. you then run the rest of your turbo plumbing as usual however you need to install one more link. in the intake stream you have to run a reversion pump, like a reverse blower. what this does is it creates two high pressure areas, the exhaust and the intake. you have to calculate it so that the turbo pressure is still enough to blow past the reversion pump. so in theory you pressurize the exhaust and the intake so when the piston is on its power stroke it becomes the low pressure area and the intake pressure fills the new low pressure area as the exhaust leaves the cylinder.
its a tuning nightmare to say the least. the turbo has to be ratioed exactly so that it builds more boost off of less exhaust pressure to make sure that it fills the cylinder with the intake charge and not just equalize with the exhaust and the intake. the guy started going into how you had to run the engine extra lean to make sure your exhaust go really hot to make sure that you could build boost because the flow was so restrictive. i stopped him there
i was getting a headache.