Timeline for Advantage of Hadamard gate over rotation about the X axis for creating superpositions
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 6, 2018 at 9:50 | history | undeleted | kludg | ||
| Aug 6, 2018 at 9:50 | history | edited | kludg | CC BY-SA 4.0 |
added 3 characters in body
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| Aug 6, 2018 at 9:48 | history | deleted | kludg | via Vote | |
| Aug 6, 2018 at 9:32 | comment | added | glS♦ | @kludg this is not true as written. Did you mean to write hermitian instead of real? | |
| Aug 6, 2018 at 9:31 | comment | added | Norbert Schuch | @kludg Why would $U=U^\dagger$ for real $U$?? This is completely wrong. Try e.g. [1 -1;1 1] (normalized) - a pi/2 rotation about Y - which doesn't square to the identity. (Indeed, a Y rotation by pi/2 prepares the same superpositions as H starting from the computational basis.) | |
| Aug 6, 2018 at 7:29 | comment | added | kludg | @NtwaliB. Ok; but most people would not overcomplicate things and just use $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ because it looks simpler. | |
| Aug 6, 2018 at 7:24 | comment | added | Ntwali B. | I would choose the one that makes the computer do the least amount of work. If a Hadamard gate is implemented in terms of rotations, I will use a rotation about X as it saves me the use of two additional gates. If Hadamard is a native gate, I will use Hadamard since most people are used to it. Note: Hadamard generates $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ while $R_x(\frac{\pi}{2})$ generates $\frac{1}{\sqrt{2}}(|0\rangle - i|1\rangle)$ | |
| Aug 6, 2018 at 7:19 | comment | added | kludg | @NtwaliB. Suppose you need just a superposition with 50% chances being $|0\rangle$ and 50% chances being $|1\rangle$; both $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ and $\frac{1}{\sqrt{2}}(|0\rangle - i |1\rangle)$ are equally good for you, but what would you choose? | |
| Aug 6, 2018 at 7:12 | comment | added | Ntwali B. | You certainly answer the question and thanks for that. Though would you mind elaborating why one would specifically need $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ over say $\frac{1}{\sqrt{2}}(|0\rangle - i |1\rangle)$? I believe elaborating on that will shed more light to aid my understanding. | |
| Aug 6, 2018 at 7:00 | history | answered | kludg | CC BY-SA 4.0 |