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# Questions tagged [pauli-gates]

For questions about Pauli matrices in general or Pauli gates in particular, as relevant to quantum computing and/or quantum information theory. The Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. The three Pauli gates are: Pauli-X gate, Pauli-Y gate & Pauli-Z gate. X = {{0,1},{1,0}}; Y = {{0,-i},{i,0}}; Z = {{1,0},{0,-1}}.

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### Gate Y returns wrong phase in IBM's circuit composer

One can check that, with IBM's circuit composer, $Y$ gate acted on $|0\rangle$ or on $|1\rangle$ returns the same phase of $\pi/2$. Is this a bug?
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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'...
318 views

### Qubit in a mix sin/cosine state

The question is pretty simple. How can I get an input qubit $|0⟩$ in the state, say $$\cos{\frac{\pi}{10}}|0⟩ + \sin{\frac{\pi}{10}}|1⟩$$ Or any other sine/cosine mix state? Which gates do I need to ...
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### How do physical implementations of Z gate selectively affect $\lvert1\rangle$ basis vector?

The Pauli Z gate inverts the phase of $\lvert1\rangle$ while leaving $\lvert0\rangle$ unaffected. When I think about how $\lvert1\rangle$ and $\lvert0\rangle$ are physically realized, however, as ...
112 views

### How does the actual measurement collapsing an error to an orthogonal basis look like?

An error can be written as a linear combination of $\Bbb I$, $X$, $Z$, $XZ$ Pauli matrices. So when measuring an errand state we aim at collapsing the error into one of these four possibilities. How ...
1k views

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### Is there a simple rule for the inverse of a Clifford circuit's stabilizer table?

In Improved Simulation of Stabilizer Circuits by Aaronson and Gottesman, it is explained how to compute a table describing which Pauli tensor products the X and Z observable of each qubit get mapped ...
442 views

### Shorthand notation for the sign flip gate

I need to use the following matrix gate in a quantum circuit: $$\text{Sign Flip}=\left[\begin{matrix}0 & -1 \\ -1 & 0\end{matrix}\right]$$ $\text{Sign Flip}$ can be decomposed as (in terms ...
### Is the Pauli group for $n$-qubits a basis for $\mathbb{C}^{2^n\times 2^n}$?
The $n$-fold Pauli operator set is defined as $G_n=\{I,X,Y,Z \}^{\otimes n}$, that is as the set containing all the possible tensor products between $n$ Pauli matrices. It is clear that the Pauli ...