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.
672
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How I can preform a unitary operation on the third qubit of the GHZ state
so I create the GHZ state already as the photo bellow
and also I preform a CNOT on the first qubit( as the target qubit),and the second qubit(as the control qubit),
then after that I have to ...
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2
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If eigenvalues of two matrices are equal then the matrices are equal?
Suppose $k_i$ and $f_i$ are eigenvalues of two density matrices A and B,
If $k_i=f_i$ then A=B?
If the answer is no, under which conditions the statement holds?
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72
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Show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \right\rangle$ is unitary [duplicate]
I am reading Quantum Computation and Quantum Information by Chuang and Nielsen and they claim that it is easy to show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \...
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Hong Ou Mandel interference and bell basis measurment
It is well known that using Hong Ou Mandel interference in polarization one can only detect 2 out of the 4 bell states($|\psi^+\rangle$ and $|\psi^-\rangle$ can be detected but $|\phi^+\rangle$ and $|\...
-1
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0
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28
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Some lemma proof related to shor algorithm
How to derive or prove Lemma A4.12 and Theorem A4.13 from appendix 4 (section 4.3) of the book Quantum Computation and Quantum Information by Michael A. Nielsen, ...
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34
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How to represent a general 3-qubit state as a symmetric ZX-diagram with 14 parameters?
A general pure 1-qubit state can be written as a ZX-diagram like this:
Correspondingly, for a general pure 2-qubit state:
How can a general pure 3-qubit state be written as a ZX-diagram?
Two things ...
- 747
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1
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65
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Clarification about the Alberti's Theorem proof given by Watrous in his condensed lecture notes
In the John Watrous condensed TQI lecture notes, an alternative proof of the Alberti's Theorem is given. He use an auxiliary lemma that states;
Lemma 4.9. Let $P \in Pos(X)$. It holds that $${inf}_{R\...
- 63
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399
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Represent Hadamard gate in terms of rotations and reflections in Bloch sphere
I read in a book that any single qubit operation can be decomposed as
$$
\bf{U} =e^{i\gamma}\begin{pmatrix}e^{-i\phi/2}&0\\ 0&e^{i\phi/2}\end{pmatrix}\begin{pmatrix}\cos{\theta/2}&-\sin{\...
- 51
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55
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How does measuring a density matrix give Kraus operators?
I am trying to complete this exercise regarding noisy channels. I need to measure a density matrix to get the Kraus operators. However, if I measure, I only get scalars. Can someone please explain how ...
- 163
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82
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Why do minimal ensemble decompositions for $\rho$ contain $|\psi⟩\in{\rm supp}(\rho)$ with probability $1/\langle\psi|\rho^{-1}|\psi⟩?$
I came across the following exercise (2.73) in Nielsen & Chuang and am trying to understand it intuitively.
Here is my reasoning of what is going on:
The purpose of this exercise:
Let’s say we are ...
- 163
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2
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53
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What is meant with "different ensembles can give rise to the same density matrix?"
I am reading the Nielsen & Chuang section on density matrices and I don't understand the example given to demonstrate a concept. Here is what I am reading:
First, they said these two different ...
- 163
1
vote
1
answer
53
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Finding the effect of conjugate transpose on a state $|b\rangle$
Say that I have a unitary gate $U$ such that $U|b\rangle=|b+1$ mod $N\rangle$. How would I go about finding $U^\dagger|b\rangle$?
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What's the Schmidt decomposition of $|\psi\rangle = 1/ \sqrt{3}( |0\rangle| 0\rangle + |0\rangle |1\rangle + |1\rangle |1\rangle)$?
$|\psi\rangle = 1/ \sqrt{3}( |0\rangle| 0\rangle + |0\rangle |1\rangle + |1\rangle |1\rangle) $
I absolutely cannot figure out the Schmidt decomposition of this state. I have looked at a ton of ...
- 21
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59
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In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?
In this book, Theorem 2.7 has the QECC conditions. I attach a snippet here
Theorem 2.7 (QECC Conditions). $(Q, \mathcal{E})$ is a $Q E C C$ iff $\forall|\psi\rangle,|\phi\rangle \in Q, \forall E_a, ...
- 13
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An Introduction to Quantum Computing Exercise 7.1.6
This question is from An Introduction to Quantum Computing Kaye et al. I'm having a difficult time coming up with a solution for this question. It is in relation to period finding however I cannot ...
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