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
2
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In Shor's algorithm, why do we have ${\rm gcd}(x\pm 1, N) > 1$?
I'm struggling to understand the last part of Shor's algorithm, to be exact the point when we found $x-1$, $x+1$ with $x-1 ≠ 0\mod N$, $x+1 ≠ 0 \mod N$ and $(x+1)(x-1) = 0 \mod N$.
Then, $gcd(x-1, N) &...
glS♦
- 25.9k
0
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1
answer
25
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Quantum Cryptography without Bell's Theorem -- Brassard - Bennett - Mermin
It is an old paper but I'm trying to understand one of their argument. They say that if
$$U|u\rangle |a\rangle = |u\rangle |a^\prime\rangle \ \ \ \mathrm{and} \ \ \ U|v\rangle |a\rangle = |v\rangle |a^...
glS♦
- 25.9k
3
votes
1
answer
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Wong's "Introduction to Classical and Quantum Computing" Exercise 7.23
I am currently working my way through "Introduction to Classical and Quantum Computing" by Thomas Wong. I am trying to solve the following problem:
Exercise 7.23. Answer the following ...
- 59.9k
0
votes
2
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How does a three-qubit state evolve through a CNOT gate?
Suppose I have a qubit which is entangled with another; let's say they are in the state
$|\psi\rangle:=A|00\rangle+B|11\rangle$.
If I have another qubit
in the state $|\phi\rangle:=a|0\rangle+b|1\...
- 2,321
2
votes
1
answer
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Wong's "Introduction to Classical and Quantum Computing" Exercise 7.20
I am currently working my way through "Introduction to Classical and Quantum Computing" by Thomas Wong. I am trying to solve the following problem on Simon's Algorithm:
Exercise 7.20. You ...
glS♦
- 25.9k
6
votes
2
answers
225
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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 ...
- 2,321
1
vote
3
answers
59
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Intro book on classical and quantum computing by Thomas G Wong
Looking at his book, and am obviously new to studying this. Could someone help explain to me how the truth table is valid here?
To my understanding, when $C=0$, the circuit behaves like a reversible ...
- 81
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votes
0
answers
57
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How I can preform a unitary operation on the third qubit of the GHZ state [closed]
So I create the GHZ state already as the photo below
$$
|\Delta\rangle=\frac1{\sqrt2}(|000\rangle+|111\rangle)
$$
and also I preform a CNOT on the first qubit (as the target qubit), and the second ...
1
vote
2
answers
157
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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?
- 7,155
-1
votes
1
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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 $|\...
- 4,449
2
votes
2
answers
84
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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) \...
- 7,155
4
votes
2
answers
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How to get the Bloch sphere angles given an arbitrary qubit?
I understand that given a pure state $ |\psi\rangle$, we can express it in terms of two angles $\theta$ and $\varphi$ such that $|\psi\rangle = \cos(\theta/2)|0\rangle + \mathrm{e}^{i\varphi}\sin(\...
- 7,155
1
vote
1
answer
158
views
How to calculate probability of measuring $|1\rangle$ after application of $R_x$ gate
I was trying to understand how to calculate
the probability of measuring $|1\rangle$ when executing the following circuit in Qiskit:
...
CommunityBot
- 1
2
votes
1
answer
59
views
When are two Hermitian operators unitarily similar?
Let $A$ and $B$ $2^n \times 2^n$ Hermitian matrices. What are sufficient and necessary conditions that they are equal up to some unitary, i.e. there exists $U$ such that $A = U B U^\dagger$?
The first ...
- 2,321
1
vote
2
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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 ...
glS♦
- 25.9k