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by zitterbewegung 3060 days ago
Gil Kalai can have his contrarian opinion on quantum computers. But we can have a much simpler argument against quantum computers. That they will remain infeasible for a long enough time for traditional computers to catch up to it.

What I mean by traditional computers catching up with it is that we will see innovations in traditional algorithms that either make quantum computers extremely pricey for a very long time in respect to traditional computers or that we find innovations that will bypass the things that they are good at without violating any of the current theories we have.

Currently, we have an enormous effort invested in our silicon architecture. We seem to be hitting limitations to silicon and they seem to be making a large bet on Quantum computers to eventually allow them to proceed. But, if quantum algorithms take a long time to have useful implementations then we have a local maxima where quantum computers aren't close enough to implement without investing a massive amount of money and that silicon just becomes cheaper and cheaper. When Intel finally reaches the limit of traditional computing that doesn't mean that it won't stop being cheaper.

Intel, IBM, Microsoft, DWave, Google and other companies have small bets on quantum computer engineering strategies that may or may not pay off. Also there seems to be a bunch of researchers publishing more and more papers on the theory of quantum algorithms. There are cross collaborations with academia on quantum computation (and they are basically what the research institutions work with the quantum engineering departments in those companies).

If we find that quantum computers can only speed up computations in the limited set of algorithms then they will probably end up as accelerator cards attached to traditional computers. I expect a order of magnitude of inefficiency to translate problems or do work on quantum computers. Either due to interconnecting or the way that we will figure out to operate them. So we will see these systems relegated to supercomputer workloads.

On the algorithms side, funding the research of quantum algorithms will probably dry up in the way that string theory research has.

Hopefully we will see a large breakthrough that will make quantum computers feasible. From my reading of the research it seems like Topological Quantum Computers have the best chance.

4 comments

> That they will remain infeasible for a long enough time for traditional computers to catch up to it.

Doesn't work for things we know are exponentially faster on quantum computers. Eventually, with enough (but not an absurd number) of bits, a decent quantum computer can solve problems that wouldn't be possible on a classical computer the size of the universe operating for billions of years.

Improvements in algorithms cuts both ways, too. And for some classes of problems, it's possible to prove (given P != NP, etc) that any classical algorithm is much worse than quantum.

We don't know of any such thing. There is nothing proven to be NP-hard that can be done in polynomial time with a quantum algorithm. Factorization isn't proven to be NP-hard.
/Proven/, sure. Hence the parenthetical "(etc)". As far as we know, however, factorization is not in P.
Your first statement isn't quite true. See, for example, https://www.scottaaronson.com/blog/?p=473

In short, it's hard to classically model pretty simple quantum mechanical systems and sample the probability distribution of outcomes. Using a quantum computer to simulate the system and sample the probability distribution is easy.

If conventional computers catch up, this might indicate that there exist conventional solutions to quantum problems. That could lead to new physics.
> Gil Kalai can have his contrarian opinion on quantum computers. But we can have a much simpler argument against quantum computers. That they will remain infeasible for a long enough time for traditional computers to catch up to it.

IIUC and IIRC (both somewhat doubtful admittedly), Feynman argued - https://people.eecs.berkeley.edu/~christos/classics/Feynman.... - that only a quantum computer can perform a scalable simulation of quantum physics. Assuming that is correct, there is no option for "traditional computers" to catch up for all problems at least.

Why are topological quantum computers more resilient? Do they handle the problem of decoherence better?
Yes, they do handle decoherence better. Here is a video explaining the theory behind the particles that are used to perform topological quantum computation [0]. I emphasize that unlike superconducting, quantum dots, ion traps, photonic e.t.c; topological quantum computers have not been physically realized because non-abelian anyons have not been detected.

[0]: https://www.youtube.com/watch?v=hKFecm9NKbM

...they have, if you believe this (fairly convincing!) set of evidence showing perfect Andreev Reflection (robust to changes in gate potential), which should only be possible (in a way robust to changes in gate potential) in the presence of Majorana states (i.e. a type of non-abelian anyon): https://quantumfrontiers.com/2017/11/21/majorana-update/
"Non-Abelian Anyons" would be a great band name. "Have Not Been Detected" would be a great 1st album name.
Yes, they are the theoretically the most elegant way to deal with decoherence. They rely on an exotic state of matter, non-abelian anyons(many still working on verifying their existence), and winding discrete non-abelian anyons into a topological braid, which disperses the quantum state spatially, making it much more resilient against decoherence(obvious simplifications made). This is the specific type of quantum computation that Microsoft is pursuing ala Michael Freedman and co.
What's interesting about topological quantum computing is that these Majorana pairs are resistant to disturbances for the same reason that Cooper pairs are in superconductors.