Questions tagged [pauli-gates]

Question 1

In Fowler's paper, "Surface codes: Towards practical large-scale quantum computation" (link), a rudimentary probabilistic model for logical errors is described. My only issue with this is ...

Question 2

In this article: http://home.lu.lv/~sd20008/papers/essays/Clifford%20group%20[paper].pdf , the author calculates the order of the Clifford group and there is one step I'm not convinced. Consider $n$ ...

Question 3

I recently noticed that some quantum computers supply native gate $$iSWAP_{\theta} = e^{-i \theta (XX + YY)}.$$ I wonder, how do I build a circuit for $$e^{-i \theta Z\otimes(XX + YY)}$$ Is this one ...

Question 4

Let $\mathcal{P}$ denote all Pauli operators (Heisenberg-Weyl operators in general). I want to see that $\frac{1}{d^4} \sum_{A_i, B_i \in \mathcal{P}} tr(A_1 U^\dagger B_1 U A_2 U^\dagger B_2 U \...

Question 5

Can you explain what is this circuit representing? it is supposed to perform measurement using Pauli operator P non destructively? How is that happening in this circuit?

Question 6

Is there a rotation operator that doesn't change the outcome probability when measuring either on basis X or Z in the scenario where I only change the sign of the angle? I was thinking of $R_y(\pm\...

Question 7

This is a follow up of this question I am getting a bit confused about how to properly build a circuit implementing Pauli exponentiation. I usually start from the standard decomposition of $e^{-i \...

Question 8

According to this paper, for a given Hamiltonian $H$ we can build (efficiently) a circuit that implements $e^{-i \epsilon Y\otimes H}$. I know how to build the circuit in case $H$ is just a single ...

Question 9

I am confused about the Pauli matrices. I am trying to decipher a statement like this: "[...]these three operators form a complete basis for the set of all unitary transformations on a single ...

Question 10

Define $\mathcal{P}_n$ to be the set of all $n$-qubit Pauli strings with phase $+1$. Then any Hermitian operator $H$ can be decomposed into linear combination of these Pauli strings. That is, $$ H=d^{-...

Question 11

I am learning how to use Qiskit's controlled Pauli gates. For example, I can create a simple three-qubit circuit containing controlled Pauli-XX and -ZZ gates using the code: ...

Question 12

Given the Hadamard gate $$H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1\end{pmatrix}$$ what are the possible values of $\sqrt H$? And what is the geometrical interpretation of $\sqrt H$...

Question 13

Suppose I run a Clifford circuit with noise and send the syndrome data to a decoder. Assume that the decoder's raw output tells me where in the circuit a particular Pauli error occurred. In this ...

Question 14

Suppose I have a state stabilized by $S = \{S_1, S_2, ... S_n\}$. I want to find another state such that it is the $+1$ eigenstate of all $S_i$ where $i \neq 1$ and the $-1$ eigenstate of $S_1$. I ...

Question 15

Consider a system of $ n $ qudits of size $ q $. Suppose that $ | \psi \rangle $ is an absolutely maximally entangled state. In other words, $ | \psi \rangle $ is a state such that the reduction to ...

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Questions tagged [pauli-gates]

Asymptotic scaling of surface codes, why p and not 2p/3?

How to prove that identical Pauli commutation relations guarantee the existence of a conjugating unitary?

What is the circuit for $e^{-i \theta Z\otimes (X X + Y Y)}$?

Simplifiying trace of Paulis

Non destructive implementation through phase estimation

Rotations that don’t change the outcomes probabilities in X and Z

Mapping Pauli exponentiation into quantum circuits

Exponentiating over sum of Paulis

On Pauli matrices being a basis for unitary transformations

Decompose a positive operator in Pauli basis

Understanding Qiskit's controlled-Pauli gates

What are the square roots of the Hadamard gate?

How to efficiently propagate the error from the decoder to the logical observable?

How to find an operator that anticommutes with exactly one stabilizer and commutes with the rest?

Prove that the entanglement definition of AME implies the error correction definition of AME

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