Timeline for Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?
Current License: CC BY-SA 4.0
10 events
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| Oct 29, 2018 at 7:33 | comment | added | Adrien Suau | @user1271772 In this case no, $\lambda$ cannot ever be negative because the QPE impose that $\theta \in [0, 1)$. If $\lambda < 0$ (because you plugged a matrix with a negative eigenvalue, this is possible of course), then the output of the QPE will not represent $\lambda$ but rather $\lambda - 2k\pi$ with $k = \lfloor \frac{\lambda}{2\pi} \rfloor$, i.e. "$\lambda$ modulo $2\pi$", and this will make the HHL algorithm fail. | |
| Oct 27, 2018 at 4:35 | comment | added | user1271772 No more free time | Let's say $t=1$. Are you saying lambda cannot ever be negative? What's wrong with having a negative eigenvalue? Let's say $k=2$ and $t=1$. Then: $0 < (\lambda / 2\pi) + 2 < 1$, and $-4\pi < \lambda < -2\pi$. A completely valid value for $\lambda = -3\pi$. What is wrong with that? Why does $\lambda/2\pi$ have to be positive or $0$ ? Eigenvalues can be negative. | |
| Aug 24, 2018 at 18:22 | history | edited | Sanchayan Dutta | CC BY-SA 4.0 |
edited title
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| Jul 6, 2018 at 11:59 | history | edited | Sanchayan Dutta |
edited tags
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| Jul 5, 2018 at 9:47 | history | edited | Adrien Suau |
new tag for HHL and QPE
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| Jul 5, 2018 at 7:01 | vote | accept | Adrien Suau | ||
| Jul 4, 2018 at 9:48 | history | edited | Adrien Suau | CC BY-SA 4.0 |
error in the last sentence.
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| Jul 4, 2018 at 9:40 | history | edited | DaftWullie | CC BY-SA 4.0 |
changed the interval notation to the one which I believe is more widely used. Feel free to revert if you disagree!
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| Jul 4, 2018 at 9:36 | answer | added | DaftWullie | timeline score: 10 | |
| Jul 4, 2018 at 9:01 | history | asked | Adrien Suau | CC BY-SA 4.0 |