Any physical quantum computer would have a limit on the fidelity with which it can create qubit superposition states. If we're trying to create $|\Psi\rangle = c_0|0\rangle + c_1|1\rangle$, the physical machine could only set $c_0$ and $c_1$ to some finite resolution, say 5 decimal places, for instance. In a trapped ion system, for example, the lasers would not be perfect, nor could they be turned on and off instantaneously, and this would create uncertainty in the qubit.

So I'm wondering how this would affect a quantum algorithm. I know of the Quantum Turing Machine, but it assumes that superposition states can be set exactly, right? Are there any models of quantum computing that postulate uncertainty in the superposition states and how this would limit any particular quantum computation?

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    $\begingroup$ It would be hilarious and pretty embarrassing if physicists hadn't thought of this ;) It's called quantum error correction and a large number of ways have been proposed or developed to implement it. $\endgroup$ – Mark Mitchison Apr 21 '16 at 7:06

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