No it doesn't. You know that the result of the computation for an individual qubit will be either 0 or 1 (otherwise it would be useless -- measuring only gives you one bit of information), so you construct the system such that after the computation is done each qubit will be aligned with the |+z> or whatever axis. The key point is that you have to be clever about how you construct the system for a given QC algorithm, not that you cannot do arbitrary computations using the system.
OK but we're back on square one. If you can't read info from qbits without breaking the state of the whole freaking system then what exactly is that you reading? Doesn't the alignment info collapses superposition?
You do "break the state of the whole freaking system". Once you've read the output, you're done. You have to set up your initial state again and run the computation from scratch.
