Why have quantum circuits won out over quantum Turing machines?
I've popped up here 7 months too late but in response to the question here's my short-ish answer: Quantum Turing machines are physically unreasonable. Prof. Peter Shor originally wrote his factoring algorithm using a Turing machine and so from a theoretical perspective they work just fine. However, it requires the tape heads to be entangled, which is why you couldn't realistically make it work. The Circuit model (which has been around longer than Turing machines) also has it's own problems which is why Turing needed his machine. One main reason (there are others) is that circuits are designed for a given input size whereas Turing machines are independent of input size. Therefore the circuit model is better suited to quantum computation as it is a more realistic reflection of the devices we could build.