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
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Why does unitary matrix acts only on input qubit state of a vector that is a result of add modulo 2?
Let $|\psi\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k \oplus b\rangle $ so that $|\psi'\rangle = \frac{1}{\sqrt{2}}[\sum_{k=2}^{1}(-1)^{ka}(U_{A}|k\rangle \otimes U_{B}|k \oplus b\rangle)]...
- 518
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What is the expression for $|\psi\rangle\!\langle\psi|$ if $|\psi\rangle=\cos(\theta/2)|0\rangle+\sin(\theta/2)e^{i\phi}|1\rangle$?
Let $|\psi\rangle = \alpha|0\rangle + \beta |1\rangle$. In Bloch sphere representation, this is
$\cos\frac{\theta}{2}|0\rangle + \sin\frac{\theta}{2}e^{i\phi}|1\rangle$.
In matrix representation:
$|\...
- 518
1
vote
1
answer
85
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Why can $(0,0,3/5,0,0,0,4/5,0,0)$ be written as $\frac35|3\rangle+\frac45|7\rangle$?
Context. $\newcommand{\qr}[1]{\left|#1\right\rangle}$ A passage from a lecture by Scott Aaronson: "As an example, instead of writing out a vector like $$(0,0,3/5,0,0,0,4/5,0,0),$$ you can simply ...
- 257
3
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2
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114
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What we get when measure $|0\rangle$ under computational basis?
It is said if we have been given the state $|0\rangle$, the measurement will yield $0$ with probability $1$ in Nielsen's book.
So here, the measurement will yield $0$ refers to we will get state $|0\...
- 639
2
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1
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85
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Does the state obtained flipping $a,b$ in the state $(a,b)^T$ have a name?
Suppose we have a qubit with a state vector of $\begin{pmatrix}
a \\
b
\end{pmatrix}
$.
If we flip $a$ with $b$ does the new qubit has a name in relation to the first qubit?
- 151
-1
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2
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Define a traceless part of $\rho$ [closed]
I saw in a paper: $|\bar{\rho}\rangle\rangle=|\rho\rangle\rangle-|\hat{I}\rangle\rangle / 2^{n / 2}$ for the $4^n$-dimensional vector representing the traceless part of $\rho$. https://arxiv.org/abs/...
- 639
3
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1
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133
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calculate the reduced density matrix of a 2 qubit state and compare the eigenvalues
So I have the exercise to apply a Cz gate to the following 2 Qubit state
$|a\rangle \otimes |b\rangle = (a_0 |0\rangle + a_1 |1\rangle) \otimes (b_0 |0\rangle + b_1 |1\rangle)\\\\$
Afterwards, I ...
- 31
1
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0
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Do solutions to the exercises in Preskill's lecture notes exist anywhere?
I'm teaching myself quantum computing and would like to know if solutions to the exercises in Preskill's lecture notes exist anywhere. It's quite hard to see if my approach is correct because I don't ...
- 165
1
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How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = \text{Tr}_{2}[\rho_{12}] = \sum_{i}\langle i_{2} | \rho | i_{2} \rangle$?
Let the system be a 2 - qubit system and let $\rho_{12}$ be a density matrix of some state for this 2 - qubit system.
How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = Tr_{2}[\...
- 518
2
votes
1
answer
137
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How to figure out whether a truth table can correspond to a valid quantum gate
I am new to quantum computing and trying to wrap my head around this exercise from Wong's introduction to classical and quantum computer.
I can interpret it mentally that first is a valid quantum ...
- 21
0
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2
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97
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Explanation of the 2.60 equation page 76 in the Nielsen and Chuang [duplicate]
In the Nielsen and Chuang book page 76, equation 2.60 says that we can rewrite the trace $$Tr(A \left|\psi\right>\left<\psi\right|)$$ as follow :
$$Tr(A \left|\psi\right>\left<\psi\right|) ...
- 67
1
vote
1
answer
334
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Can a unital channel not be mixed unitary?
How to prove that for a multi-qubit system a unital channel is not necessarily mixed unitary? This is Problem 8.3 in Nielsen and Chuang. Here's a snippet of the text:
Shall I need to take two ...
- 43
4
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1
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113
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How do I find the reduced density matrix of a system where two people share one qubit and have one qubit of their own?
I have the following problem and have attempted to find a solution to it, but to no avail.
Alice and Bob have one qubit each, say $|\psi\rangle$ with Alice and $|\phi\rangle$ with Bob. They also share ...
- 165
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3
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140
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Exercise 4.16 in the Nielsen & Chuang book
In the 4.16 exercice in the Quantum Computation and Quantum Information (Michael A. Nielsen & Isaac L. Chuang), I don't understand why the correct answer is not this matrix :
$$
\left[ {\begin{...
- 67
5
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2
answers
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What are "completely positive" and "CPTP" quantum maps?
I am studying quantum computing a little bit by myself, and I have simple questions.
I didn't find a clear definition of what is a completely positive and trace-preserving (CPTP) map. The best I've ...
- 185