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I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

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Re: I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

#142

Earlier quoted context omitted.

Sure it makes sense - a qubit is canonically a quantum spin system, which has two eigenstates, up and down.

What about superposition? Or is that not considered a 'state'?

They're states but not eigenstates. It's like the difference between RGB colour and greyscale. In both cases there are infinitely many possible colours, but in greyscale they're all mixtures of two "primary" colours (black and white) whereas in RGB they're mixture of four (black, red, green and blue).

In a qubit the infinitely many superposition states are all mixtures of just two eigenstates.

Re: I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

#143

Earlier quoted context omitted.

Sure it makes sense - a qubit is canonically a quantum spin system, which has two eigenstates, up and down.

What about superposition? Or is that not considered a 'state'?

A superposition is indeed a state, comprised of linear combinations of the basis states.

Further, (and anyone, please correct me where I'm wrong), the eigenfunctions (which could actually be called eigenstates) of an operator ARE the basis set, as they are orthonormal. (Right?)

Re: I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

#145
post #3

Hi Scott, Shtetl-Optimized's tagline is famously "Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once". What phrase do you think should replace 'trying all the possible solutions at once' in the public conciousness as a succinct description of the mechanisms of a quantum computer? Or is this topic simply too complex to be distilled into a neat syn…

Exactly the question I would love answered. Edit: this seems roughly answered to a question by user r4um

I don’t see where it’s answered?

Re: I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

#149
post #3

Hi Scott, Shtetl-Optimized's tagline is famously "Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once". What phrase do you think should replace 'trying all the possible solutions at once' in the public conciousness as a succinct description of the mechanisms of a quantum computer? Or is this topic simply too complex to be distilled into a neat syn…

I'll just point to this https://www.smbc-comics.com/comic/the-talk-3 which was posted as an answer to a similar question I had on a previous discussion about a blog post of his.
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