While I fully empathize with having a child who is an undaunted explorer, and commend you for having door alarms installed, I agree with the responses from other posters.
There are huge liability issues with a parent taking their eyes off of a child "for two minutes" in a public setting, leaving the child unsupervised. Eclipsing that is the potential for permanent harm or early death for your child, by unsupervised exploring whether at home or in public.
If your child has not had the usual scraped knee or other minor injuries, he may not have a context or frame of reference for pain, and therefore may have an unrealistic sense of safety. However when a minor injury occurs, to acquaint him with simple facts of safety you may wish to begin mentioning that some injuries are small and will heal, while others are bigger and may never heal.
Teaching your wandering two-year-old about stranger danger may also be worth considering.
I'm also familiar with parents having told their children that "it's the law" that children must stay with their parents, and that if children are found wandering unsupervised, the parents may be declared unfit and the children taken away.
These are just a few ideas. It is up to parents to determine whatever you think your child will understand and respond to with the positive behavior of valuing supervision.
That being said, rather than feeling badly or having fear of being labeled a bad parent, it may be more positive to chalk this up to a learning experience and realize that a child with a propensity to explore needs close and mindful supervision. This may be a part of the reason why parents of gifted children often report feeling exhausted and sleep-deprived... and may be part of the bond among many gifted parents.
