After you quit, you can absolutely compete with them. The only issue around "owning the idea" is with regards to patents. Having personally gone through this, it is hard (perhaps impossible) for them to claim patent assignment on a patentable idea that hasn't already been filed with the patent office before your end date. Once you leave the company, preparing the patent application would be work which you can not be forced to do. They also can't file since they weren't the inventors.