All Questions
Tagged with pauli-gates universal-gates
6 questions
2
votes
0
answers
44
views
What class of matrices have efficient decompositions?
Suppose we have an arbitrary matrix $A \in \mathbb{C}^{N \times N}$ where $N=2^n$. Now suppose that we can decompose $A$ into tensor products of the Pauli basis given by $A=\sum_{l=0}^Lc_lS_l$ where $...
- 565
3
votes
0
answers
68
views
Trying to prove Theorem 4.1 from Nielsen and Chuang algebraically
Background
Theorem 4.1 of Nielsen and Chuang (10th Anniversary Edition) states how a universal single-qubit unitary can be constructed from Y and Z rotations.
Suppose $U$ is a unitary operation on a ...
- 31
3
votes
1
answer
2k
views
construction of Y gate from X,Z and H gates
As a part of textbook exercise, Y gate is to be constructed using H,Z and X-gates, just like we have $X = HZH$. is there some way/process/intuition to find such combinations or it is just like we need ...
- 587
4
votes
0
answers
100
views
What is the correct name of this quantum gate? Possibly state control gate
Let $\vec v \in \mathbb{C}^2 $ be the following quantum state:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
- 41
2
votes
2
answers
663
views
How do I create an inverse identity gate?
Is it possible for me to construct a gate that inverse everything ($|0\rangle \rightarrow -|0\rangle, |1\rangle \rightarrow -|1\rangle$, etc. basically like a $-I$ gate) from the basic $X, Y, Z, CX,......
- 604
6
votes
2
answers
2k
views
controlled-Z rotation gates in symmetrical fashion
I was going through the qiskit textbook and in this chapter I came across a statement under the topic "Kickback with the T-gate" related to the Controlled-Z gate that
the controlled-Z ...
