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Comment by peepeepoopoo101 | Hacker News Reader

There's an awful lot of handwaving in this blog post. I'm sorry, but I'm not convinced. The author mentions how some devices that can seemingly solve exponential time complexity problems also require exponentially high precision, but there doesn't seem to be a strong argument for why that doesn't apply to quantum computers. We haven't experimentally demonstrated quantum computing at sufficient scales to prove that the required number of physical qubits to perform error correction doesn't scale exponentially.

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I got the impression that DJB was criticizing the arguments for why quantum computers won't work. Not trying to demonstrate why they will work.

yup

We don’t need exponentially more physical qubits because we have quantum error correction schemes that exponentially decrease the logical error rate with only a polynomial increase in the number of qubits. There are in fact many schemes for this (https://errorcorrectionzoo.org/) with the surface code mentioned in the blog being a leading approach.

Details for how this could work for factoring are here: https://arxiv.org/abs/1905.09749

There will be engineering challenges to scale up these implementations but in principal you shouldn’t need exponential resources (unless there is something wrong with quantum mechanics). This sort of error correction scaling does not exist, for example, for analog computing.

The author is DJB.

For those not familiar: https://en.m.wikipedia.org/wiki/Daniel_J._Bernstein

I think you've missed the point of it then.

Note that you do not need error correction for quantum computing. You only need it for digital quantum computing. There's a separate branch, analog quantum computing, that is also very promising.

Does anybody want to elaborate why I'm being downvoted?

For context, there are several companies selling analog quantum computers, e.g. Pasqal, D-Wave.

What D-Wave has is not a quantum computer, in the sense that it (the computer architecture) can't solve BQP problems efficiently. They are widely considered shills by the quantum computing community.

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