All Questions
Tagged with pauli-gates circuit-construction
15 questions
0
votes
1
answer
60
views
Pauli Twirling not increasing Circuit depth?
This paper talks about the properties of Pauli twirling a circuit. Pauli twirling is a technique that converts arbitrary quantum noise into Pauli errors by applying random Pauli gates before and after ...
- 25
2
votes
2
answers
155
views
CX and CZ commutation
Suppose I have control qubits $1$ and $2$ and target qubit $3$. I have the circuit element
$$E = CX_{1-> 3}CZ_{2-> 3}$$
I would like to swap the order and have
$$E' = CZ_{2-> 3}CX_{1-> 3}$$...
- 23
1
vote
1
answer
82
views
Exponentiating a tensor product of operators acting on disjoint qubit registers
Consider a problem of implementing $\operatorname{e}^{i\bigotimes_j O_j}$, where all the $O_j$ terms act on disjoint sets of qubits.
Assume that efficient circuits implementing individual $\...
- 2,221
1
vote
1
answer
101
views
How to interpret the encoding circuit for the 5-qubit QECC
I have a question on circuit which constitutes the sydnrome measurement for the 5-qubit error correcting code. If I focus on just a portion of the circuit:
Reference for image. The full circuit can ...
- 739
4
votes
0
answers
64
views
Efficient quantum algorithms to decompose Hessian matrices into sums of unitaries
Are there efficient quantum algorithms that given a d-sparse hessian $H \in \mathbb{C}^{N \times N}$ decompose it into a sum of unitaries (e.g. Pauli matrices)?
$$H = \sum_i^q a_i U_i$$
If an ...
- 361
5
votes
2
answers
1k
views
Commutation rules between Pauli $X$ and controlled-Hadamard
Are there any known commutation rules between the $X$ gate and the $CH$ gate?
- 2,058
6
votes
2
answers
1k
views
How to perform a controlled Pauli string rotation gate?
I would like to know some circuit decomposition for an arbitrary controlled Pauli string rotation:
\begin{equation}
|0\rangle\langle 0| \otimes e^{i \theta (P_1\otimes...\otimes P_n)}+ |1\rangle\...
- 583
1
vote
1
answer
83
views
Can we design a circuit that outputs desired estimates?
If we have state $\lvert\psi\rangle \in (\mathbb{C}^{2})^{\otimes n}$ in an $\textit{n}$-qubit system with Pauli operators $P$ such that $P \in \{I, X, Y, Z\}^{n}$, how can we design a circuit/...
- 173
1
vote
2
answers
157
views
Is it true that $Ry(\pi/2)\sigma_zRy(-\pi/2)=\sigma_x$?
I saw in a qiskit document that said $Ry(\pi/2)\sigma_zRy(-\pi/2)=\sigma_x$ To confirm this I decided to create the matrix representations of these operations and multiply them together to see if I ...
- 145
7
votes
3
answers
3k
views
Why isn't $Ry(\pi/2)$ gate equivalent to Hadamard gate?
I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together.
Speaking in terms of simulations using qiskit,...
- 189
3
votes
1
answer
2k
views
Controlled Z gate using Pauli rotation operators and Z tensor product Z
I am trying to construct a controlled Z gate using elementary gates. This is what I have so far: \begin{pmatrix}
-i & 0 & 0 & 0\\
0 & -1 & 0 & 0\\
0 & 0 & 1 & 0\\
...
- 31
6
votes
3
answers
120
views
How to create the state $\vert 0 \rangle+i \vert 1 \rangle$ using elementary gates?
I am trying to write $|0\rangle+i|1\rangle$ in terms of elementary gates like H, CNOT, Pauli Y, using the IBM QE circuit composer.
I was thinking some kind of combination of H and Y since $Y|0\rangle=...
- 121
2
votes
2
answers
663
views
How do I create an inverse identity gate?
Is it possible for me to construct a gate that inverse everything ($|0\rangle \rightarrow -|0\rangle, |1\rangle \rightarrow -|1\rangle$, etc. basically like a $-I$ gate) from the basic $X, Y, Z, CX,......
- 604
6
votes
1
answer
2k
views
How can I simulate Hamiltonians composed of Pauli matrices?
Suppose I want to perform the time-evolution simulation on the following Hamiltonians:
$$
H_{1} = X_1+ Y_2 + Z_1\otimes Z_2
\\
H_{2} = X_1\otimes Y_2 + Z_1\otimes Z_2
$$
Where $X,Y,Z$ are Pauli ...
- 2,408
3
votes
1
answer
228
views
Can you take infinitely many square roots of Pauli-X?
I am trying to find the cost for a n-bit Toffoli gate based on the recurrent circuit presented on Barenco's Work in Lemma 7.5 (Elementary gates for quantum computation)
The construction requires that ...
