All Questions
Tagged with textbook-and-exercises hadamard
30
questions
5
votes
2
answers
403
views
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
$$
\bf{U} =e^{i\gamma}\begin{pmatrix}e^{-i\phi/2}&0\\ 0&e^{i\phi/2}\end{pmatrix}\begin{pmatrix}\cos{\theta/2}&-\sin{\...
- 51
2
votes
5
answers
470
views
How to eliminate the global phase of a state vector?
Say that I have a qubit that began in the $|0\rangle$ state and then the
Hadamard gate is applied, resulting in the following state:
$ \begin{bmatrix}
\frac{1}{\sqrt{2}} \\
\frac{1}{\sqrt{2}}
\end{...
- 143
2
votes
1
answer
407
views
Decomposing Hadamard gate
I'm following a lesson, and it says that the Hadamard gate can be decomposed to three gates: RZ(pi/2), squared root Z, and RZ(pi/2). However, when I do matrix multiplication of these three matrices, I ...
- 119
1
vote
1
answer
335
views
How do you write the Hadamard operator on two qubits in braket notation?
I understand how to write the Hadamard operator on one qubit in braket notation using $$\newcommand\bra[1]{\left\langle#1\right|}\newcommand\ket[1]{\left|#1\right\rangle} H=\sum_{i,j} \bra{w_{j}}H\ket{...
- 631
2
votes
1
answer
70
views
In general, what is feasible quantum computation?
I don't really understand what is feasible quantum computation, in my book (Lipton and Regan's Quantum Algorithms via Linear Algebra) they said that:
A quantum computation $C$ on s qubits is feasible ...
- 103
3
votes
2
answers
183
views
What is $HTHTH\left| 0 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.33 (page 108):
Exercise 2.33. Answer the following:
(a) Calculate $...
- 164
4
votes
2
answers
218
views
What is $H\left| \psi \right>$ with $\left| \psi \right> = \alpha\left| 0 \right> + \beta\left| 1 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.29 (page 107):
Exercise 2.29. Say $\left| \psi \right> = \alpha\left|...
- 164
1
vote
1
answer
115
views
Equivalence between quantum circuit: CNOT changes control and target qubit
It's know that the following two circuits are equal.
In fact, answers for this can be found on wikipedia, and on this website. However, I am looking for a more formal answer. I'd like to see the ...
4
votes
3
answers
4k
views
How to represent the Hadamard gate as a rotations on the Bloch sphere?
I am new to Quantum Computing, and I have decided to try and learn the quantum gates. I am trying to understand how to represent some basic gates as rotations on the Bloch Sphere. I was able to ...
- 165
1
vote
1
answer
175
views
Simon's Algorithm: Calculating the effects on the second Hadamard gate and the resulting amplitudes
I am currently reading about Simon's algorithm in "An Introduction to Quantum
Computing" and stumbled over Exercise 6.5.1, that ask the reader to show that:
Let $\textbf{x}, \textbf{y} \in \...
- 133
2
votes
1
answer
181
views
How to apply the Hadamard gate to a given qubit state?
I have this qubit state:
$$ H \left[ \frac{1}{\sqrt{2}} |0\rangle + \left( \sqrt{\frac{2}{7}}+\frac{1}{\sqrt{7}}i \right) |1\rangle \right] $$
How to solve this given Hadamard gate on qubit?
Hadamard ...
- 79
3
votes
1
answer
477
views
How to derive the rotations caused by the H gate?
In Nielsen and Chuang, there's the following paragraph:
The Hadamard operation is just a rotation of the sphere about the ˆy axis by 90◦, followed by a rotation about the ˆx axis by 180◦.
I am ...
- 669
0
votes
1
answer
111
views
Doing $|0\rangle$ then Hadamard gate then measurement
I am starting to use quantum experience and following exactly first example from lecture. After initializing the qubit to $|0\rangle$, then applying a Hadamard gate, the probability for measuring $|1\...
- 21
4
votes
1
answer
651
views
How do you represent a Hadamard gate as a product of $R_x$ and $R_y$ gates?
I'm looking for a representation of Hadamard gate that uses only $R_x(x)$ and $R_y(y)$ gates. The values $x$ and $y$ may be the same, but they don't necessarily need to be.
- 43
2
votes
2
answers
2k
views
Is the tensor product of 2 Hadamard gates entangled?
Assume that you have a system of two qubits in the state $|11 \rangle$. Apply $H \otimes H$, where $H$ is the Hadamard matrix. Is the state $(H \otimes H)|11\rangle$ entangled?
I know if we take the ...
- 187