Quantum Computing and the Hidden Subgroup Problem
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Quantum Computing and the Hidden Subgroup Problem
1–10 of 14 posts
Re: Quantum Computing and the Hidden Subgroup Problem
#2I’m afraid I couldn’t follow. Too long since I used most of those terms or symbols.
Can anyone ELI5?
Re: Quantum Computing and the Hidden Subgroup Problem
#3I’m afraid I couldn’t follow. Too long since I used most of those terms or symbols. Can anyone ELI5?
Claude summed it up like this:
The Hidden Subgroup Problem (HSP) is the mathematical framework that explains why quantum computers are so good at breaking encryption. Famous quantum algorithms like Shor's (for factoring numbers) and Simon's are all just different versions of solving the same underlying pattern-finding problem. The quantum "superpower" comes from using the Quantum Fourier Transform to reveal hidden mathematical patterns that classical computers can't efficiently find.
Re: Quantum Computing and the Hidden Subgroup Problem
#4I’m afraid I couldn’t follow. Too long since I used most of those terms or symbols. Can anyone ELI5?
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.
Re: Quantum Computing and the Hidden Subgroup Problem
#5I’m afraid I couldn’t follow. Too long since I used most of those terms or symbols. Can anyone ELI5?
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/all useful quantum algorithms.
Re: Quantum Computing and the Hidden Subgroup Problem
#6I’m afraid I couldn’t follow. Too long since I used most of those terms or symbols. Can anyone ELI5?
A crude explanation might be like this - if you look at graphs of sin and cos, you'd instantly recognize their symmetries, but what if you're given the graph of a linear combination of them, and asked to decipher the coefficients?
Naively, you'd evaluate the functions at every point by trial & error until they much the shape of the given graph. Or use the symmetry of sin & cos to combine them constructively and destructively (peaks and valley) and to match the given shape.
FT & QFT are "shortcuts" that help to decipher the correct combination of basis functions.
Re: Quantum Computing and the Hidden Subgroup Problem
#7Can quantum computers solve hard problems that aren’t HSPs?
Re: Quantum Computing and the Hidden Subgroup Problem
#8Earlier 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…
That's very pedantic, like saying "computers don't solve integer addition, AND/OR/NOT/XOR gates solve it, those are the fundamental thing".
Re: Quantum Computing and the Hidden Subgroup Problem
#9Earlier quoted context omitted.
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…
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.
Re: Quantum Computing and the Hidden Subgroup Problem
#10Fantastic 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.