BQP is generally expect to be the correct abstraction of "quantum polynomial time," but two practical issues will need to be overcome in order to build quantum computers for realsies: the instability of quantum memories, and the error-prone nature of specific implementations of quantum gates.  In principal, both issues can be overcome, via quantum error correction and fault tolerant quantum computing, respectively.  We won't discuss fault tolerance in much detail, but will spend a little bit of time looking at quantum error correction.  As we will see, topology is a nice source of quantum error correcting codes.