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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• 209
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Connection between a Pauli measurement and the corresponding Pauli gate?

Suppose I have a qubit and the ability to act a Pauli $Z$ gate on it. This is a black box that does the phase flip and I don't know how it works on the inside. Can I use this black box to implement a ...
1 vote
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Multi-qubit quantum channels in Pauli-Liouville basis: Tensor product of Pauli-Transfer Matrices?

I would like to verify something, need a sanity check. Are the quantum channels for different qubits in the Pauli-Liouville basis (Pauli Transfer Matrices) also given by a tensor product? The Kraus ...
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• 2,913
1 vote
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Measuring a single-qubit PauliZ using Qiskit's EstimatorQNN

I am currently working with the EstimatorQNN from Qiskit to construct a Quantum Neural Network using a custom Parametrized Quantum Circuit. But I want to change the ...
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1 vote
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How to find density matrix of 3 qubit W state?

Given a state in bra-ket notation as $|\psi\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$. What is the density matrix of this state written using Pauli's spin operator?
1 vote
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How to prove that these equations are correct for $CZ$ and $CX$?

How do I prove that the equation on the right is $CX$ and $CZ$ gate? I don't think that reaching the matrix of the CX or CZ is possible with the given equation. For (b) I keep getting $I \otimes I$ ...
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Efficient way to calculate trace of product of Pauli string and matrix?

Basically the title, but more formally: is there a way to efficiently calculate the trace of the product of a Pauli string $P$ and a $2^n \times 2^n$ matrix $M$? That is, is there a way to calculate ...
1 vote
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tricks to finding possible stabilisers for $|GHZ_{3} \rangle$

The famous 3 - qubit Greenberger, Horne and Zeilinger state: $|GHZ_{3} \rangle = \frac{1}{\sqrt{2}}[|000\rangle + |111\rangle]$. A stabiliser for $|GHZ_{3} \rangle$ is the 3 - tensor product X Pauli ...
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1 vote
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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 \...
229 views

Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)

In Litinsky's paper, there are many circuits relations, like the one below. The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the ...
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As per this schematic of qubits, how this explanation is correct --"If you look again at the four possible sums, you’ll notice that there is only one case for which this is 1 instead of 0: 1+1=10....
1 vote
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Can any Qiskit circuit be converted to a gate?

I am trying to convert the following qiskit QuantumCircuit to a gate using to_gate() method. ...
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Visualizing Y-gate operation to achieve quantum state

In the below snippet how qc.y(1) helps to achieve the quantum state $i|10\rangle$ ? ...
411 views

How to prove the matrix identities $HXH = Z$ and $HZH = X$?

As we know Hadamard gates are used to bring quantum bits into superposition states. I’m trying to understand how identities $HXH = Z$ & $HZH = X$ w.r.t rotation.
1 vote
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A question on the structure of the Clifford group

Let $P_n$ be the Pauli group on $n$ qubits defined by $P_n=\{i^k \sigma_1...\sigma_n: k=0, 1, 2 \; \mathrm{or}\;3, \sigma_j\in \{I, X, Y, Z\}\}$, where $I, X, Y, Z$ are Pauli matrices. The Clifford ...
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Algorithm for Mutually Unbiased Basis Sets Available?

I'm looking for an implementation or a slightly more efficient algorithm for finding optimal Mutually Unbiased Bases (MUB). What I mean here are MUBs in terms of Pauli Strings as described here. There ...
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Finding the rotation angle $\theta$ of a 2x2 unitary matrix

We can represent a 2x2 unitary matrix as follows: $$U = \cos(\theta)I - i \sin(\theta) \vec{n} \cdot \vec{\sigma},$$ where $\vec{n} \in \mathbb{R}^3$ and $\vec{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$...
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Why is the error propagation by the CNOT gate considered without taking into account the state?

In the syndrome measurement circuit of a stabilizer code, I think you would consider that Pauli errors propagate through the CNOT gates. I don't understand why one usually considers the propagation of ...
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1 vote
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G-twisted Pauli twirl circuit

Pauli twirls are obtained by taking a unitary $U$, and finding some Pauli gates $P_1, P_2$ such that $P_1 U P_2$. So, for example, one possible twirl of the $S$ gate would be $YSX$. In the paper ...
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1 vote
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How is the definition of $n$-qubit Pauli group derived?

The authors give the following definition for the Pauli group in the paper Averaged circuit eigenvalue sampling. The n-qubit Pauli group $P_n$ consists of n-fold tensor products of single-qubit Pauli ...
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Recovering phases in $2n$-bit binary representation of n-qubit Paulis

I am currently going through a paper discussing Pauli sampling strategies for VQE: https://arxiv.org/abs/1908.06942 I want to code and test their strategy. They explain how to create a circuit ...
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Commutation relationship and measurement results

There are things I do not understand about the following circuit, and I would appreciate it if you could explain. ...
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In surface codes and color codes, when the code distance is $d$, you can correct up to $[(d-1)/2]$ Pauli errors. I would like to know what this $[(d-1)/2]$ Pauli errors means for $X$, $Y$, and $Z$. ...