Given any initial condition or value A, A leads to B after a procedure of physics or nature P. Now is there any turing machine or quantum computer that can simulates P,converting A into B? In other word, is any cause-effect relation in nature computable?
As far as we know, yes. This is essentially the Church-Turing thesis. Note that this is not a mathematical result, but more of a definition of what it means to be computable. You can find plenty of discussions about this around. A few notable examples are: