All Questions
Tagged with textbook-and-exercises quantum-gate
89
questions
1
vote
3
answers
59
views
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 ...
- 11
2
votes
2
answers
84
views
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) \...
- 121
1
vote
1
answer
53
views
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 $U^\dagger|b\rangle$?
- 63
0
votes
2
answers
73
views
Help finding mistake when modifying $T$ injection protocols
I am a little confused about where I am going wrong when computing the action of the following circuit:
My understanding is that the CNOT gate acts on the second qubit as a control and the first ...
- 631
-2
votes
1
answer
76
views
Measuring probabilities of 0 or 1 in a two qubit state
I'm preparing for my upcoming exam, I need to determine the probabilities with which Bob measures 0 or 1 and in both cases describe the state of Alice, this is my state:
$$
|\psi\rangle =\frac{1}{\...
- 1
6
votes
2
answers
225
views
Decomposition of a $4 \times 4$ unitary matrix
I am currently studying the paper "Decomposition of unitary matrices and quantum gates (2012)" and referring to the textbook Quantum Computation and Quantum Information. Among the topics, I ...
- 131
0
votes
1
answer
300
views
The expectation values for the values of both qubits [closed]
Let’s consider the two-qubit state
|Ψ⟩ =(1/2)|00⟩ + i(√3/4)|01⟩ +(3/4)|10⟩.
a) Find the expectation values for the values of both qubits separately.
1
vote
0
answers
36
views
Why does unitary matrix acts only on input qubit state of a vector that is a result of add modulo 2?
Let $|\psi\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k \oplus b\rangle $ so that $|\psi'\rangle = \frac{1}{\sqrt{2}}[\sum_{k=2}^{1}(-1)^{ka}(U_{A}|k\rangle \otimes U_{B}|k \oplus b\rangle)]...
- 518
2
votes
1
answer
137
views
How to figure out whether a truth table can correspond to a valid quantum gate
I am new to quantum computing and trying to wrap my head around this exercise from Wong's introduction to classical and quantum computer.
I can interpret it mentally that first is a valid quantum ...
- 21
1
vote
3
answers
140
views
Exercise 4.16 in the Nielsen & Chuang book
In the 4.16 exercice in the Quantum Computation and Quantum Information (Michael A. Nielsen & Isaac L. Chuang), I don't understand why the correct answer is not this matrix :
$$
\left[ {\begin{...
- 67
2
votes
1
answer
324
views
How to go from matrix to bra-ket representation of the CNOT?
I have the following definition for CNOT gate form my notes:
I am trying to derive the bracket notation form the matrix version, can someone help me to see where I am going wrong:
$$U ̂_{CNOT} ...
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
0
votes
1
answer
125
views
What state do you get applying the pauli Y gate to $|\pm\rangle$? [duplicate]
I know it's a basic question but what state gives when you apply pauli $Y$ gate over states $+$ and $-$?
If I apply $Y|+i⟩ = |+i⟩$ or $Y|0⟩ = i|1⟩$, but I don't understand what do you get when you do $...
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