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Quantum Computing since Democritus by Scott Aaronson

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7 Randomness

In the last two chapters, we talked about computational complexity up till the early 1970s. Here, we'll add a new ingredient to our already simmering stew – something that was thrown in around the mid-1970s, and that now pervades complexity to such an extent that it's hard to imagine doing anything without it. This new ingredient is randomness.

Certainly, if you want to study quantum computing, then you first have to understand randomized computing. I mean, quantum amplitudes only become interesting when they exhibit some behavior that classical probabilities don't: contextuality, interference, entanglement (as opposed to correlation), etc. So we can't even begin to discuss quantum mechanics without first knowing what it is that we're ...

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