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Results tagged with mathematics
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user 8746
DO NOT use this tag. Use more specific tags such as [linear-algebra] instead.
2
votes
1
answer
104
views
How to correctly define $U_\omega$ for Grover's search algorithm
I am working on Grover's algorithm and I am trying to implement the algorithm. I am following the Microsoft quantum katas and I finished and did everything correctly. I am trying to implement the algo …
- 887
1
vote
How do I apply a matrix to a ket state?
To add onto KAJ226's answer, you can see that $|00\rangle, |01\rangle, |10\rangle, |11\rangle$ form the computational basis. You can also see that since there is a $1$ in only one coefficient of the v …
- 887
1
vote
1
answer
871
views
Effect of Pauli X gate on minus state using bloch sphere
As I understood, the X gate flips the state around : $X(|0\rangle) = |1\rangle$. It can also be visualized with a $\pi$ rotation around the $x$ axis in the Bloch sphere. I have no problem with that.
…
- 887
5
votes
1
answer
1k
views
How can you decompose Grover's diffusion operator into gates?
I know how Grover's diffusion operator works ($U_s = 2|s\rangle\langle s|-I$) with the inversion around the mean. However, I want to implement it in simpler gates, to use the algorithm. How can I do t …
- 887
8
votes
Accepted
How can you decompose Grover's diffusion operator into gates?
Grover's diffusion operator can be implemented with H, X and a controlled Z gate. I will show this mathematically. Since $|s\rangle = |+\rangle^{\otimes n} $ :
$$
U_s = 2|s\rangle\langle s|-I = H^{\ot …
- 887