1:40 AM
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I’m trying to grok quantum walks, and would like to create an example that walks a perfect binary tree to find the one and only marked leaf node. Is this possible? If so, suppose the depth of the tree is five. Would that require a circuit with five wires? Would it best be realized with a Discrete...

@user1271772 re: "There have been proposals for exploiting certain types of phenomena that would lead to devices even more powerful than quantum computers." could u elaborate?

3 hours later…
5:08 AM
@meowzz: It's not so interesting. Born's rule guarantees that there's only 2-way interference in quantum mechanics. Think of a 2-slit experiment: |psi_1 + psi_2|^2 = |psi_1|^2 + |psi_2|^2 + (psi_1*)psi_2 + psi_1(psi_2*). Now if we have 3-slits we don't get anything more powerful, work out |psi_1 + psi_2 + psi_3|^2 and you will still only get terms that have at most 2 factors. You will not get a 3-way interference term like (psi_1)(psi_2)(psi_3).
But we know quantum mechanics is not complete because it's incompatible with general relativity, so some people think of generalizations of Born's rule where P = |psi|^(2+epsilon) for some small epsilon. Now you can have 3-way interference. Now you can have something more powerful than a quantum computer.

2 hours later…
7:16 AM
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Most of us on this site believe that quantum computing will work. However, let's play devil's advocate. Imagine that we suddenly hit some fundamental stumbling block that prevented further development towards a universal quantum computer. Perhaps we're limited to a NISQ device (Noisy, Intermediat...

7:58 AM
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The intuition I have for why quantum computing can perform better than classical computing is that the wavelike nature of wavefunctions allow you to interfere multiple states of information with a single operation, which theoretically could allow for exponential speedup. But if it really is jus...

This thread is so much cringe...phew

1 hour later…
9:16 AM
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The quantum phase estimation algorithm (QPE) computes an approximation of the eigenvalue associated to a given eigenvector of a quantum gate $U$. Formally, let $\left|\psi\right>$ be an eigenvector of $U$, QPE allows us to find $\vert\tilde\theta\rangle$, the best $m$ bit approximation of $\lflo... 9:55 AM @DaftWullie Thanks for your answer on quantumcomputing.stackexchange.com/questions/2604/… . I'll wait until the end of the day to see if someone else has something to say, but your answer satisfy me and will probably be the accepted one :) It's a nice theorem on eigenvalues! I was not aware of its existence ^^ 2 hours later… 11:31 AM Hey, I'm trying to explain to a colleague how Shor's period finding works, and in the example I've picked a random N (15) and a random a (7), now I went on to explain how the Quantum Fourier Transformation works like a clock/thumbtack, where we note down the direction each time a certain value passes... in my example the period r = 4. But you'll quickly see that the clock labelled '2' also has the exact same direction each time. How does this work? Why will the answer be 4 instead of 2? 1 hour later… 12:35 PM @RoyvanRijn Well, this is a good beginner level explanation: You could ask your question on the main site I'd be happy to answer it here, but I'm stuck up in some other work 1 hour later… 2:03 PM 0 As a non-mathematician/software programmer I'm trying to grasp how QFT (Quantum Fourier Transformation) works. Following this YouTube video: https://www.youtube.com/watch?v=wUwZZaI5u0c And this blogpost: https://www.scottaaronson.com/blog/?p=208 I've got a basic understanding on how you can ca... 1 As a non-mathematician/software programmer I'm trying to grasp how QFT (Quantum Fourier Transformation) works. Following this YouTube video: https://www.youtube.com/watch?v=wUwZZaI5u0c And this blogpost: https://www.scottaaronson.com/blog/?p=208 I've got a basic understanding on how you can ca... 4 hours later… 5:48 PM 0 I want to express the square root of NOT as a time-dependent unitary matrix such that each$n$units of time, the square root of NOT is produced. More precisely, I want to find a$U(t_0,t_1)$such that$U(t_0,t_1) = \sqrt{NOT}$, if$t_1-t_0=n$for some$n$. One possible solution is to express$...