All Questions
Tagged with pauli-gates measurement
23 questions
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Eigenvalues of Pauli Gate and connection to measurement
Suppose I measure a qubit in the $Z$ basis. If I measure and obtain the outcome $+1$, I get the post-measurement state $\vert 0\rangle\langle 0\vert$ and if I measure and obtain the outcome $-1$, I ...
- 47
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111
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What is the connection between an observable and a gate?
I am reading some introductory quantum mechanics and I don't understand the connection between an observable and a gate. I thought a gate just applies a rotation to a state while a measurement gives ...
- 23
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42
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How can I measure qutrits in the X basis using cirq?
I attempted to create a custom measurement class which, in my case, allows us to go from the z basis to x basis using a hadamard gate transformation, and then we measure wrt that new basis. However, ...
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Moving pauli product rotations past measurements
I'm trying to understand how the clifford + T compiler works in "A Game of Surface codes".
How do I move a pauli product rotation block past a pauli product measurement block? More ...
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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 ...
- 3
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Action of below circuit using heisenberg representation
Can someone please explain how the above gate affects logical operators? My understanding is that the circle indicates that we are measuring the second qubit?
My initial guess is that it is equivalent ...
- 739
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407
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Half Adder using CNOT Gates
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....
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The Output of Transversal Bell Measurement in Knill's Method of Fault-Tolerant Error Correction (FTEC)
On page 26 of this paper (arXiv), it is written that in Knill's method of fault-tolerant error correction (FTEC), the output of the transversal bell measurement becomes $(P_m \otimes I) | \Phi_0 \...
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3
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486
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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 ...
- 111
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122
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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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- 101
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Measurement in X basis
There is something I don't understand about measurement in other basis than the Z-Pauli Basis.
If measurement fixes the state of a quantum system thus destroying superposition, how can we get a ...
- 436
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545
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What does "commuting operators can be measured simultaneously" mean?
I want to understand better what it means by any commuting set of operators can be measured simultaneously.
Suppose I have an $n$-qubit arbitrary pure state $\rho = \lvert \psi \rangle \langle \psi \...
- 525
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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 ...
- 1,459
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108
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Cliffords to Transform into Common Eigenbasis
Say I have the following Hamiltonian (given in terms of Pauli operators):
\begin{equation}
H=aX_1Z_2+bZ_1X_2.
\end{equation}
Both Pauli terms commute with each other. I want to make a measurement of $\...
- 474
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Can you measure sums of Paulis in the stabilizer formalism?
Suppose we wanted to measure the observable $Z_{1} + Z_{2} + \cdots + Z_{N}$ in a stabilizer state. Is it possible to do this using only Clifford operations, and possibly adding some auxiliary qubits?
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- 215
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803
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Measuring tensor products of Pauli operators
Is there a neat way to derive and efficiently implement a measurement circuit for tensor products of arbitrary Pauli operators like $XZZXZ$ in Qiskit ?
I tried using the ...
- 88
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823
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In what sense are Pauli matrices measurement operators?
Neilson and Chuang's textbook shows a nice example of measuring in the $Z$ basis on page 89 in section 2.2.5. The Hermitians for measuring in the $Z$ basis, $|0\rangle\langle 0|$ and $|1\rangle\langle ...
- 1,459
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Measurement on a specific basis and proof of circuit output
I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
- 493
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768
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If the eigenvalues of $Z$ are $\pm1$, why are the computational basis states labeled with "$0$" and "$1$"?
The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate
\begin{equation}
Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{...
- 143
3
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2
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675
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What is the state of a qubit after measuring some a Pauli operator?
I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $ |\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle $.
From my understanding, if one ...
- 155
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2k
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Why can I apply $HS^\dagger$ and then measure in the computational basis to measure $Y$?
I come from a CS background
I was reading Neven and Farhi's paper ("Classification with Quantum Neural Networks on near Term Processors"), and I am trying to implement the subset parity problem using ...
- 147
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2k
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Physical Interpretation of Pauli Matrices as Polarization Check
We know that the Pauli matrices are:
$$\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \sigma_y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}, \sigma_z = \begin{bmatrix}1 & ...
- 1,785
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How does the actual measurement collapsing an error to an orthogonal basis look like?
An error can be written as a linear combination of $\Bbb I$, $X$, $Z$, $XZ$ Pauli matrices. So when measuring an errand state we aim at collapsing the error into one of these four possibilities. How ...
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