As others have said, the encoding of the laws does not itself mean they won't work or will be less effective in any given technology (e.g. quantum computing).
A quantum computing scenario doesn't introduce any specific way to void such rules. What would possibly happen is that the rules are, themselves, quite complex to implement and that can introduce possible errors in implementation.
First off, we have to be able to recognize a human. I can think of humans that have trouble accepting that other people are human, so I can imagine no end of possible errors in recognizing a human. A particular issue might arise in detecting when an AI is communicating with an AI - is the AI human or an AI ? What if it looks like a human ?
The whole idea of how an AI will recognize that what it may be about to do can cause harm is so complex that it's practically certain to fail sometimes. Again, humans have been interpreting their environment for a long, long time and we often get that stuff wrong, so in an AI of any kind it's probably doomed to fail sometimes.
So I'd suggest the failure mechanism is possibly one of over-reliance. I would suggest that, very typically, we design machines and then start believing they're flawless. The longer they go without failure, the more we believe they won't. When, after some time, they do, we tend to make excuses for the system as we have invested financially and emotionally in it's success.
A quantum computer could be an example of such a system. It will probably be vastly more complex than we can directly understand. It would certainly require some confidence, and an AI based on some future quantum computing technology might inspire more confidence than it warrants.
If we encode the laws somehow, then will we be willing to accept that we got it wrong ?
Could we even determine that there is a flaw ? We have trouble figuring out that humans have personality flaws, how do you figure out an AI has a flaw and is not working they way you told it to ?
The rules for such an AI would almost certainly not be formally encoded (i.e. like with formal logic). They would require the solution of fuzzy problems and prediction of cause and effect in a complex environment. These require pattern recognition applied in a very complex and general manner. I don't think any formal language would ever achieve this. The extra complexity of quantum systems simply makes it harder to detect potential flaws in the implementation of any algorithms.
In this sense, quantum computing could introduce a layer of complexity that makes flaws more likely, or at least more complex flaws harder to avoid.
The other way around the three laws is to do what humans normally do : complicate them.
As sure as blazes if we had AIs and implemented three laws in a robust way, some idiot (most likely a lawyer or an insurance type or a bureaucrat) will insist on amending them to include provisions for rules that are not really needed but they want to cover themselves. They might introduce provisions like "unless they're criminals" or "unless the damage caused saving the human will be beyond a certain cost" or that old favorite "unless national security is involved" (and a good bet on that one being forced on everyone !).
So the three laws can be broken by simply introducing the fools they're meant to protect.