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Question 1

0votes

1answer

49views

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

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 ...

Arya K

41

askedNov 9 at 15:10

Question 2

1vote

2answers

253views

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

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 $n$ ...

cos

79

askedSep 12 at 14:38

Question 3

2votes

1answer

95views

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

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 ...

Daniele Cuomo

2,173

askedAug 21 at 11:02

Question 4

2votes

0answers

107views

Simplifiying trace of Paulis

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 \...

user1577744

63

askedJun 17 at 11:57

Question 5

1vote

1answer

162views

Non destructive implementation through phase estimation

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?

Arjun Sigdel

11

askedJun 8 at 16:33

Question 6

0votes

2answers

105views

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

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\...

Daniele Cuomo

2,173

askedMay 29 at 13:07

Question 7

0votes

1answer

89views

Mapping Pauli exponentiation into quantum circuits

This is a follow up of this questionI 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 \...

Daniele Cuomo

2,173

askedMay 23 at 8:15

Question 8

1vote

2answers

128views

Exponentiating over sum of Paulis

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 ...

Daniele Cuomo

2,173

askedMay 20 at 9:01

Question 9

3votes

2answers

489views

On Pauli matrices being a basis for unitary transformations

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 ...

Matyas

167

askedApr 21 at 7:42

Question 10

6votes

1answer

369views

Decompose a positive operator in Pauli basis

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^{-...

cos

79

askedApr 13 at 5:23

Question 11

1vote

1answer

180views

Understanding Qiskit's controlled-Pauli gates

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:...

Medulla Oblongata

309

askedApr 10 at 16:59

Question 12

2votes

2answers

429views

What are the square roots of the Hadamard gate?

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 $\sqrt H$...

Matteo Vitturi

181

askedMar 1 at 23:09

Question 13

2votes

2answers

197views

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

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 ...

juno

23

askedJan 12 at 16:52

Question 14

3votes

2answers

339views

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

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 ...

hugo

33

askedJan 10 at 16:07

Question 15

3votes

1answer

258views

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

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 ...

Ian Gershon Teixeira

5,498

askedDec 16, 2024 at 23:17

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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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