Questions tagged [textbook-and-exercises]
Applies to questions of primarily educational value - styled in the format similar to that found in textbook exercises. This tag should be applied to questions that are (1) stated in the form of an exercise and (2) at the level of basic quantum information textbooks.
675
questions
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Measuring probabilities of 0 or 1 in a two qubit state
I'm preparing for my upcoming exam, I need to determine the probabilities with which Bob measures 0 or 1 and in both cases describe the state of Alice, this is my state:
$$
|\psi\rangle =\frac{1}{\...
- 1
1
vote
1
answer
154
views
Is a linear combination of unitaries unitary?
Suppose you have a pure state $\vert\psi\rangle$. Consider the following operation.
For unitaries $U_1$ and $U_2$, one can take complex numbers $\alpha, \beta$ where $|\alpha|^2 + |\beta|^2 = 1$ and ...
- 3,085
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1
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45
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Calculate of theoretical probabilities for the outcomes
I have a $|+\rangle$ state qubit and I measure it in a random basis. The random basis is made with random $\theta$, $\varphi$ and $\lambda$ of $U3$ gate. How can I calculate the theoretical ...
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2
votes
0
answers
53
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Measuring an entangled quantum state
I have this exercise to solve, but I can't figure out how to proceed.
First, I don't think the state proposed is valid (the probabilities don't sum up to 1).
'Secondly, given that it should be an ...
- 29
0
votes
0
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31
views
Deriving a equation in "Data re-uploading for a universal quantum classifier" paper: U(phi1,phi2,phi3) U(x1,x2,x3) = U(theta + w *x)
In "Data re-uploading for a universal quantum classifier" paper the U(phi1,phi2,phi3) U(x1,x2,x3) is derived as U(theta + w *x) in compact state.
How to derive the above equation ?
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1
vote
1
answer
38
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Is qiskit.pulse.SamplePulse deprecated?
I'm currently following along the book "Learn Quantum Computing with Python and IBM Quantum Experience" by Rodert Loredo and I am at chapter 8 - Generating pulse schedules on hardware. The ...
1
vote
2
answers
98
views
Why $\sqrt{\rho} = P \sqrt{\rho}$ in the proof of quantum error correction conditions in Nielsen & Chuang?
I have trouble understanding a proof in Nielsen & Chuang, specifically the identity in (10.20), which reads $$ U_k^\dagger P_k F_l \sqrt{\rho} = U_k^\dagger P_k^\dagger F_l P \sqrt{\rho}.$$
By ...
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6
votes
2
answers
225
views
Decomposition of a $4 \times 4$ unitary matrix
I am currently studying the paper "Decomposition of unitary matrices and quantum gates (2012)" and referring to the textbook Quantum Computation and Quantum Information. Among the topics, I ...
- 131
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votes
1
answer
199
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How to show that the GHZ state is absolutely maximally entangled?
A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
5
votes
1
answer
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Question about Nielson & Chuang Problem 9.2
I am working on the following problem from the book "Quantum Computation and Quantum Information" by Nielsen and Chuang.
Problem 9.2: Let $\mathcal{E}$ be a trace-preserving quantum
...
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3
votes
1
answer
107
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Why is the operator $M_a |x\rangle= |a \cdot x \pmod{N} \rangle $ unitary?
If $N\geq 2$, $a\in \mathbb{Z}_N$, and $a^r= 1$ for some $r$. Consider the operator $M_a$, which is related to order finding :
$M_a |x\rangle= |a \cdot x \pmod{N} \rangle $ if $x\in \mathbb{Z}_N$
What ...
- 51
0
votes
2
answers
77
views
Why is a density matrix an orthogonal projector?
Suppose I have a density matrix like $\rho = \frac{1}{2}[I + \hat{n}\vec{\sigma}]$.
The claim is that $\rho$ is an orthogonal projector for the state $|+\rangle$ in an arbitrary direction $\hat{n}$.
...
- 518
1
vote
0
answers
67
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Possible post - measurement states for Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$
This is in reference to page 241 of Introduction to classical and quantum computing by Thomas.G Wong.
The author starts off with a Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$.
In trying ...
- 518
3
votes
2
answers
123
views
How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
- 57
0
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1
answer
300
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The expectation values for the values of both qubits [closed]
Let’s consider the two-qubit state
|Ψ⟩ =(1/2)|00⟩ + i(√3/4)|01⟩ +(3/4)|10⟩.
a) Find the expectation values for the values of both qubits separately.
