In this rather speculative note three problems pertaining to the power and limits of quantum computing are posed and partially answered: a) when are quantum speedups possible?, b) is fixed-point computing a better model for quantum computing?, c) can quantum computing trespass the Turing barrier? 1 When are quantum speedups possible? This section discusses the possibility that speedups in quantum computing can be achieved only for problems which have a few or even unique solutions [12]. For instance, this includes the computational complexity class UP [15]. Typical examples are Shor's quantum algorithm for prime factoring [18] and Grover's database search algorithm [13] for a single item satisfying a given condition in an unsorted database (see also Gruska [14]). In quantum complexity, one popular class of problems is BQP,whichisthe set of decision problems that can be solved in polynomial time (on a quantum computer) so that the correct answer is obtained with probability at l...