Let's say the halting point and a few other points which uniquely identify the control flow of a program are known in advance.
Is there a computer architecture which would be able to execute such a program faster than a normal computer?
Is neural computation the only way?
If so, why aren't we using brains with an electronic interface for computation, and write software on them which can be executed much faster?

Why bother with computers when brain tissue is the best computing device to ever exist?