Comment by vtomole | Hacker News Reader

Comment by vtomole | Hacker News Reader

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> Is there a place for quantum computers if classical algorithms become more capable at simulating quantum mechanics in ways we find useful?

There is not. Our existence as a field pretty much hinges on classical computers not being able to simulate all quantum mechanical problems efficiently. We imagine that designing quantum matter: https://cognitivemedium.com/qc-a-science, https://arxiv.org/abs/1508.02595 will be very useful in the scientific and technological sense and we don't think classical computers will ever fully stand up to that task.

> Breaking crypto, unless that falls too

If classical computers can simulate quantum efficiently then using quantum computers to break crypto also falls. Simulating quantum physics and factoring are in the same complexity class: https://en.wikipedia.org/wiki/BQP

> Our existence as a field pretty much hinges on classical computers not being able to simulate all quantum mechanical problems efficiently.

I don't think this is quite accurate. It could be that many of the kinds of quantum simulations we care about can be done efficiently classically, even if the worst-case quantum simulations are classically intractable. Certainly, classical simulation algorithms are steadily improving.

Right. We are now arguing over the nuances of what would make quantum computers useful, which I address in a comment where I say "Everything matters" later in this thread.

Most people who work in this field doubt that every quantum simulation problem we care about will be classical tractable in practice, that is, non worst-case. If we believed that, we might as well give up and continue to use the robust, mature classical computers we have and will continue to have better instances of for the foreseeable future.

I don't put too much stock into complexity classes. They're a real thing for sure, but implementation difficulties and constant factors are too.

I agree. "Everything" matters when it comes to these applications: complexity theory, heuristics, constant factors, quantum error correction overhead, qubit quality, improvements in classical algorithms, CPU and GPU improvements e.t.c. Doesn't make sense to put too much stock in just one of these components at the cost of others.

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