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.
Questions tagged [textbook-and-exercises]
649 questions
2
votes
1 answer
Exercise 1.1 in Quantum Processes Systems, and Information
I was going through Quantum Processes Systems, and Information by Benjamin Schumacher and Michael Westmoreland and could not understand the very first exercise which goes like
Exercise 1.1 Identify at least seven distinct physical representations…
seeker
- 159
- 2
1
vote
1 answer
Can we rearrange terms in the tensor product?
Define $o = A \otimes B$. Compute the results of $o^{\otimes N}$. We have
\begin{align}
o^{\otimes N}
&= (A \otimes B) \otimes (A \otimes B) \otimes ... \otimes (A \otimes B).
\end{align}
Can we groups the terms A and terms B and…
Michael.Andy
- 559
- 2
- 7
1
vote
2 answers
How does one begin to map a circuit to this problem? (Reversible 2-bit demultiplexer using NOT, CNOT, Toffoli & Fredkin)
I am relative beginner to building qc circuits and programming. Please share with me how you would begin to approach this problem. What steps would you take to draw this circuit? Thank you for your help.
What I have worked on thus far:
I have…
sivaguru42
- 11
- 2
1
vote
1 answer
How to write the state $|ψ\rangle=|00\rangle+\sqrt{i}|01\rangle+(3+i)|11\rangle$ as a column vector?
Consider the two-qubit state $|ψ \rangle= 1|00\rangle +\sqrt i |01\rangle + (3+i)|11\rangle$. How can I write the state $|\psi\rangle$ as a column vector? I'm confused.
And what if I want to measure in the $Z$-basis, what are the probabilities of…
n22
- 183
- 5
1
vote
1 answer
How to prove that tensor products of two pure density operators is again pure
I came up with an intuitive guess that tensor product $\phi\otimes\psi$ of two pure states $\phi,~\psi$ (which are density operators) is again pure. However, I tried to use basic linear algebra and proved nothing. Should I use Schmidt composition?…
Shara
- 165
- 4
0
votes
2 answers
An Introduction to Quantum Computing - Exercise 6.4.1
The Exercise 6.4.1 from Kaye et al. is as follows
Prove that $$\bigg({|0\rangle +(-1)^{x_1}|1\rangle
\over\sqrt{2}}\bigg)\cdot\bigg({|0\rangle +(-1)^{x_2}|1\rangle
\over\sqrt{2}}\bigg)\cdots\bigg({|0\rangle +(-1)^{x_n}|1\rangle …
afarouz
- 1
- 1
0
votes
1 answer
How does a three-qubit state evolve through a CNOT gate?
Suppose I have a qubit which is entangled with another; let's say they are in
$A|00\rangle+B|11\rangle$.
If I have another qubit
in the state $a|0\rangle+b|1\rangle$ then the combined state is…
0
votes
1 answer
did i calculate the matrix elements correctly?
Suppose the below operator
$$
x\sum_{n=0}^{\infty}\tanh^{2n}(r)|0,n\rangle\langle 0,n|
+y\sum_{n=0}^{\infty}\tanh^{2n}(r)|1,n\rangle\langle 1,n|
+z\sum_{n=0}^{\infty}\tanh^{2n}(r)(n+1)|1,n\rangle\langle…
reza
- 689
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- 9
0
votes
1 answer
On the Conjugate Transpose Problem of Composite Systems
I've tried two quantum computing textbooks
"QUANTUM COMPUTING From Linear Algebra to Physical Realizations" and "quantum information and quanutum computing"
, and most only have a lot of discussion on single quantum systems and less on composite…
Ren-Xin Zhao
- 536
- 3
- 12
0
votes
1 answer
What’s the point of the amplitudes being complex?
I understand that Introducing complex numbers to the amplitude allows us an extra degree of freedom. Through the rotation of the complex vector, you can encode the same magnitude (1/√2) with an infinite number of configurations around a circle. The…
Vinay Sharma
- 509
- 1
- 12
0
votes
1 answer
How can I compute $P_{|b\rangle}(|0\rangle)$?
I've just started to learn Quantum Computing and, to do it, I'm reading the course "Introduction from Quantum Computing" by IBM.
Now, I'm reading the chapter "Entangled states", section "Product states" where they show how to compute the probability…
VansFannel
- 177
- 5
-1
votes
1 answer
Derivation explanation needed
I'm pretty new to the field. I was reading Preskill Ph219 course notes and came across this. I am a bit confused about the derivation and wondered if someone can write down some skipped steps here.
thongn98
- 3
- 1
-1
votes
1 answer
Why the equality regarding Kronecker delta holds?
Can anyone show me why this equality below holds? I understand the matrix form of Kronecker delta is an identity matrix, but why this "coming from nowhere" delta function $\delta_{i,j}$ can have the exact same index $(i, j)$ as the previous…
Guannan Guo
- 3
- 1
-1
votes
1 answer
probability of measuring 1 in a qubit in a state
Imagine we prepare a qubit in the following state :
$$ |\psi\rangle = \sqrt{\frac{1}{3}}|0\rangle - \sqrt{\frac{2}{3}}|1\rangle$$
What is the probability of measuring 1?
Emma
- 11
-2
votes
1 answer
In the context of Quantum theory of Information, Typical eigenvectors are permutations of basis vectors. Why?
Why is this so? Can someone please give me detailed steps with an explanation?
user07
- 31
- 2