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Tagged with pauli-gates terminology-and-notation
9 questions
1
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2
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Notation: Hamiltonian Simulation of Pauli Gates
Let $\sigma^j_x$ describe the following unitary over $n$ qubits: on the $j$-th qubit, it acts as the Pauli $x$ operator; instead, on any other qubit, it acts as the identity. A paper states now that
\...
- 73
4
votes
1
answer
121
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In what contexts are different notations used for indicating measurement outcomes?
I have seen a few different notations for denoting measurement outcomes. Does anyone know of which notation is more widely used in various contexts?
For instance, I like referring to this Wikipedia ...
- 1,459
4
votes
0
answers
100
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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:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
- 41
8
votes
2
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1k
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What is (formally) a transversal operator?
This question concerns about a formal definition of transversal operator.
I understood that transversal operator are a group of operators which are efficient in terms of circuit depth and can be used ...
- 2,058
9
votes
3
answers
346
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Is there a convention for denoting $Y$ eigenstates?
Two common shorthands for eigenstates of the $Z$ operator are $\{|0\rangle,|1\rangle\}$ and $\{|1\rangle,|-1\rangle\}$, where in the first case we have $Z|z\rangle=(-1)^z|z\rangle$ and in the second ...
- 1,038
5
votes
2
answers
768
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If the eigenvalues of $Z$ are $\pm1$, why are the computational basis states labeled with "$0$" and "$1$"?
The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate
\begin{equation}
Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{...
- 143
6
votes
2
answers
1k
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What are boost and shift operators and why are they called so?
In some texts I see $X$ and $Z$ Pauli operators as being said as boost and shift operators respectively.
But I came across some text that defines its own operators, namely:
$$
X \vert j\rangle = \...
- 61
3
votes
1
answer
351
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What does the notation $\sigma_j^z$ mean for Pauli matrices?
In multiples papers or online article on the QAOA algorithm (such as this one), I found notation for the Hamiltonian similar to this one :
$$ \sum_{ij} \frac{1}{2} (I-\sigma_i^z \sigma_j^z)$$
I don'...
- 583
6
votes
2
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2k
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How to compute the average value $\langle X_1 Z_2\rangle$ for a two-qubit system?
Show that the average value of the observable $X_1Z_2$ in a two-qubit system measured in the state $(|00\rangle + |11\rangle)/\sqrt{2}$ is zero.
How would we approach this question? I understand that ...
- 163