# 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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### Transform Pauli basis to other basis

The Pauli basis is \begin{align} I=\left[\begin{matrix} 1&0 \\ 0&1 \end{matrix} \right], \end{align} \begin{align} X=\left[\begin{matrix} 0&1 \\ 1&0 \end{matrix} \right], \...
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### Pauli decomposed Hamiltonian as Diagonal U gate

While trying to implement a quantum circuit, I had to apply Hadamard gates to all qubits to achieve equal superposition. Done. The next operation is decomposing the Hamiltonian into a sum of tensor ...
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### Express $e^{i\frac{\gamma}{2}Z\otimes Z}$ in terms of CNOT and rotations gate

I have the Hamiltonian evolution operator for a two qubit system : \begin{equation} \hat{U}= e^{-i\gamma H}\;,\quad H = \frac{1}{2}(I - Z\otimes Z) \end{equation} where the $Z$ gate is applied on both ...
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### Algorithm for finding Pauli stabilizers of a code

Given the zero logical $|0_L\rangle$ and one logical $|1_L\rangle$ for an $[[n,1,d]]$ code is there a well known/ efficient algorithm for determining which Pauli operators stabilize the code?
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### Expectation values of non-local operators in Qiskit

Is there a convenient way in Qiskit to calculate the expectation value for a non-local operator, i.e. I would like to calculate: $$\langle \Psi|O|\Psi \rangle$$ More precisely, I would like to ...
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1 vote
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### Check if a Pauli string belongs to a stabilizer tableau

Given a Pauli string and a stabilizer tableau, how do I know that the Pauli string belongs to the tableau, i.e. can be written as a product of strings already in the tableau. Thanks.
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### Equivalence check between rotational gates and Pauli gates

My question is highly related to this one. I am trying to understand the relationship between rotational gates $R_P(\theta)$, where $P \in \{X,Y,Z\}$. As stated here, $\exp(iPx)=\cos(x)I+i\sin(x)P$. ...
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### Calculate $\sqrt{X}$ for the Pauli $X$ gate

I was trying to build a $cccx$ gate. According to this paper by Berenco et al., it requires a $\sqrt{X}$ gate. Furthermore, I found another paper by Muradian and Frias with this formula: \sqrt A=\...
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### Confirming locality of a Hamiltonian through decomposition

I was trying to understand Trotterization. The given Hamiltonian is decomposed into a sum of $k$-local Hamiltonians which can be exponentiated in $O(1)$ gate complexity. After which the Trotter ...
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### Direction of rotation for single-qubit unitary operators

The rotation operators for a single qubit are defined as $R_{v}(\theta) = e^{-i \theta X/2}$, with $v \in \{ X,Y,Z\}$. If we look at the direction of rotation of $R_v$ w.r.t. the positive eigenvalue, ...
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### How to obtain the state $|0\rangle+|1\rangle$ from $|0\rangle$ via Pauli gates?

Could somebody explain in which way are we able to achieve superposition with Pauli $X$, $Y$, $Z$ matrices? In case of Hadamard gate $H$ we change coefficients to $1/\sqrt{2}$ directly, in case of $X$ ...
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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 ...
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### Decompose into completely stabilizer preserving channel in surface codes

In the article "Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise" they are talking about decomposing (possibly ...
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### Convert Coherent Noise to Clifford Errors with Probability on Surface Codes

Following my question about the equivalence of coherent and no coherent error, in surface codes. Now I understand, it is not equivalent. I tried to read some articles about it, and I couldn't find a ...
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### Commutation rules between Pauli $X$ and controlled-Hadamard

Are there any known commutation rules between the $X$ gate and the $CH$ gate?
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