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Quantum Computing and the Hidden Subgroup Problem
11–14 of 14 posts
Re: Quantum Computing and the Hidden Subgroup Problem
#12Earlier quoted context omitted.
That's very pedantic, like saying "computers don't solve integer addition, AND/OR/NOT/XOR gates solve it, those are the fundamental thing".
> That's very pedantic Yes because we're talking about pure math here not popcorn and soda.
My attempt at less offensive analogies:
"Efficiency of hw arithmetic is not the bottleneck, lack of a poly time algo to factor prime numbers is"
&, the closely related
"Ability to reduce everything to HSP is not the bottleneck, lack of a scaleable implementation of qFT is"
Re: Quantum Computing and the Hidden Subgroup Problem
#13Fantastic writeup! The exposition is extremely clear. I particularly appreciate the choice of Simon's Algorithm as a "toy example" and the quick recap of character theory; both were very helpful for a non-QC person with an interest in this stuff.
Thanks!
Re: Quantum Computing and the Hidden Subgroup Problem
#14Earlier quoted context omitted.
I think it would be hard to explain the details to a math undergraduate. The high level point is that many algorithms for which quantum speedups are possible can be reduced to the Hidden Subgroup Problem, which requires a few weeks of a group theory course to understand.
No it wouldn't? "Given f that hides a subgroup, and an oracle for f, determine the subgroup". The Wikipedia phrases it backwards (as do you): "quantum computers" don't solve the hidden subgroup problem, the quantum fourier transform, which "measures" f in parallel, can be used to solve the hidden subgroup problem efficiently. The QFT is the fundamental thing, not the HSP, and it's the building block for basically any…
Very late, but I meant it would be hard to summarize the details of the blog post (e.g. QFT implementation) even to the typical math undergraduate.
It's not hard to explain the problem, as most math undergraduates will have taken some group theory course. But even "subgroup" means nothing to most computer scientists (speaking from personal experience interacting with computer scientist academics).