# 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}}.

186 questions
Filter by
Sorted by
Tagged with
175 views

### Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not

In Exercise 10.40 of Nielsen and Chunang's textbook, the reader is supposed to construct an inductive proof of Theorem 10.6 that any Clifford gate can be made of Hadamard, phase and c-not. There it is ...
34 views

### Phase estimation of the Pauli-Y matrix

I'm trying to use the phase estimation algorithm to extract the eigen value for both eigen vectors of the Pauli-Y matrix using the ibm quantum experiance. So far I have this for the possitive state |+&...
21 views

50 views

### Rotation of qubit - Pauli Gates XYZ

I don't understand how to apply a Pauli Gate on a qubit. Lets say 8 got a qubit with in state: $$|\psi\rangle = 0.891 |0\rangle+ 0.454i |1\rangle$$ How would I compute e.g. rotating it 90 degrees ...
1 vote
25 views

### Conjugating pairs of Paulis to each other with a non-entangling Clifford

This a follow-up question to Conjugating pairs of Paulis to each other with a Clifford We call a Clifford gate local if it is a tensor product of single qubit Clifford gates. We call a Clifford gate ...
157 views

60 views

### 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 ...
2k views

### Qiskit CNOT-gate matrix mixup?

In the qiskit textbook chapter 1.3.1 "The CNOT-Gate" it says that the matrix representation on the right is the own corresponding to the circuit shown above, with q_0 being the control and ...
1 vote
103 views

### 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.
63 views

### 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, $\exp(iPx)=\cos(x)I+i\sin(x)P$. ...
1 vote
88 views

### Decomposing a projector in the computational basis in terms of Pauli matrices

I have a $x \in \mathbb{N}$, and I would like to decompose it in terms of the Pauli matrices $\sigma_x, \sigma_y, \sigma_z$ and the identity. My first steps are as follows:  \begin{align} |x \...
99 views

### 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 vote
285 views

### How to decompose a multi qubit Clifford unitary into a sequence of clifford gates

What are the algorithms that allow to decompose any given multi qubit Clifford unitary into elementary Clifford operations (e.g. Pauli+CNOT, with no T gate)?
31 views

### Does anybody know what a low-degree Markov field is?

In the paper Fast Estimation of Sparse Quantum Noise I saw the following description: quantum devices approaching the fault-tolerant regime will have very few significant errors (and therefore are ...
638 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 ...
1 vote
478 views

### what is Pauli twirling approximation?

In this video, Artur Ekert shows that for a single qubit, 4 Kraus operators can be chosen such that the action on state $\rho$ is given as $\rho \rightarrow \sum_m p_m A_m \rho A_m^\dagger$. We can ...
211 views

Suppose we have an $n$-qubit system. Let $Y_i$ and $Z_j$ denote the Pauli-Y and Pauli-Z operators acting on the $i$th and $j$th qubits, respectively. Suppose we have a finite set of tuples $E = \{(i,j)... 1 vote 2 answers 304 views ### What are the Pauli-Y eigenvectors? The question should be pretty simple, but it turns out that there's more to it with respect to what I initially expected. Starting from the definition of the gate$Y = \begin{bmatrix} 0 & -i \\ i &...
Since the Pauli Z gate equate to a rotation around z axes of the Bloch sphere by $\pi$ radians, the phase of anything that lies on z axes is expected to change by $\pi$ by applying z-gate. As $|0⟩$ ...
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, ...