Only two months and now it runs like this? I've read about this exact problem on other carb'ed ZXs here. You could try searching to see how they were resolved. Without knowing the history of that particular bike, I think generally that the recommendation will be to drain and pull the float bowls off for a cleaning.
It's probably an obstruction in/with:
Pilot air screws
pilot jet
float needle sticking/blocked/fuel munge
jet needle/main jet
flat slides stuck
or something that was disassembled recently regarding vacuum/ignition/fuel
If you're familiar with carbs and a little mechanically inclined, you can buy some B-12 carb cleaner and blow the carb intake and jet holes out and verify if there was an obstruction somewhere.