Timeline for How do I check if a gate represented by Unitary $U$ is a Clifford Gate?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 17, 2022 at 5:39 | comment | added | quest | @CraigGidney I guess I am done with that. Juts confused with np.dot and @ one more time | |
| May 17, 2022 at 1:47 | comment | added | quest | @CraigGidney Could you give an example for a 8*8 matrix? (or 4*4 ) So that I can see what I am missing. I am trying do this method for my matrix (which is also 8*8) but probably missed something and I do not want to open a topic for the same question. | |
| Aug 4, 2020 at 13:36 | comment | added | Craig Gidney | @vasjain The matrices have size 2^n by 2^n, so multiplying them naively has cost O((2^n)^3) = O(8^n). You do this O(n) times. Everything else is less expensive. | |
| Aug 4, 2020 at 8:01 | comment | added | vasjain | I apologize, I didnt follow the complexity analysis. Could you explain it in a more detail as how you reached $O(8^N)$ and $2N$. | |
| Aug 3, 2020 at 19:54 | comment | added | Craig Gidney | Note that you do need to check that the Paulis you inferred from the first column actually reproduce the rest of matrix. | |
| Aug 3, 2020 at 19:08 | comment | added | Craig Gidney | Look at the first column of the matrix. It should have exactly one non-zero entry. The row of that entry in binary tells you which qubits got Pauli X operations. Then conjugate the matrix with Hadamards and repeat the same trick to get the locations of Pauli Zs. There's a lot of leeway here as it's not nearly as expensive as the matrix multiplication step. | |
| Aug 3, 2020 at 17:59 | comment | added | vasjain | How would you check if a matrix is Pauli Product | |
| Aug 3, 2020 at 17:31 | history | answered | Craig Gidney | CC BY-SA 4.0 |