How do I cut short my notice period?

I have mostly been doing a lot of experimental/skunkwork at my current organisation and decided to switch and got a job offer. Gave my resignation, and now I want to cut short my notice period so that I can join the other place sooner. The upper management isn’t really happy about this and they might give me some QA QC work or some other rubbish pet project. How do I get out of this, without burning bridge?