# Questions tagged [nielsen-and-chuang]

For questions about exercises or passages from the popular quantum computing textbook *Quantum Computation and Quantum Information* by Michael Nielsen and Isaac Chuang.

121 questions
Filter by
Sorted by
Tagged with
63 views

### In Nielsen and Chuang, how can $\frac{1}{2(e-1)}$ result from $\frac12\int_{e-1}^{2^{t-1}-1}dl\frac{1}{l^2}$?

From Nielsen and Chuang's book: $\textit{Quantum computation and quantum information}$, how can (5.34) equal (5.33)? I.e. $$\dfrac{1}{2} \int_{e-1}^{2^{t-1}-1} dl \dfrac{1}{l^2} = \dfrac{1}{2(e-1)}.$$...
42 views

284 views

### Nielsen&Chuang 5-qubit quantum error-correction encoding gate

$\newcommand{\bra}{\left<#1\right|}\newcommand{\ket}{\left|#1\right>}\newcommand{\bk}{\left<#1\middle|#2\right>}\newcommand{\bke}{\left<#1\middle|#2\middle|#3\right>}$ In ...
62 views

### Does composition of two single qubit rotations yield a single rotation around a unit vector?

$\newcommand{\coefcos}{c_1 c_2 - s_1 s_2 \hat{n}_1 \cdot \hat{n}_2} \newcommand{\coefsin}{s_1 c_2 \hat{n}_1 + c_1 s_2 \hat{n}_2 - s_1 s_2 \hat{n}_2 \times \hat{n}_1}$This question relates to ...
48 views

### Show that for any measurement operator $M_m$ there exists unitary $U_m$ such that $M_m=U_m\sqrt{E_m}$ with $E_m$ POVM

Exercise 2.63 of Nielsen & Chuang asks one to show that if a measurement is described by measurement operators $M_m$, there exists unitary $U_m$ such that $M_m = U_m \sqrt{E_m}$ where $E_m$ are ...
30 views

### Where do errors occur during error syndrome and recovery?

I'm studying quantum error correction on Nielsen's Quantum Computation and Quantum Information, but I don't understand how it identifies the number of places where an error may occur. It uses ...
38 views

### Deformation of the Bloch sphere and contraction of its planes under the action of channels

On pg 376-377 of N&C, it gives 3 different diagrams showing how the various axis of the Bloch sphere will be contracted under the action of the channels, limiting the possible states after it's ...
149 views

### Nielsen & Chuang Exercise 2.55: Prove that $\exp \left[ -\frac{iH(t_2 - t_1)}{\hbar} \right]$ is unitary

$\newcommand{\expterm}{\frac{-iH(t_2 - t_1)}{\hbar}} \newcommand{\exptermp}{\frac{iH(t_2 - t_1)}{\hbar}}$Nielsen & Chuang (10th edition, page 82) states that $H$ is a fixed Hermitian ...
120 views

### Is there any 'official' list of errata for Nielsen & Chuang?

The book Quantum Computing and Quantum Information by Nielsen and Chuang is a well-known and celebrated text book that can act as a resource in a wide variety of topics. Of course, in such a vast ...
73 views

253 views

### Procedures and intuition for designing simple quantum circuits?

I'm working my way through one of the quantum circuits sections in Nielsen and Chuang and I'm struggling to get a feel for the basics of circuit construction. For example, one of the exercises is as ...
64 views

### Correct Formulation of N&C Exercise 4.11 and other textbooks misquoting

Inspired by the comments in this question How to approximate $Rx$, $Ry$ and $Rz$ gates?, there is the errata for question 4.11 pg 176 in N&C. The original form states that for any non parallel $m$ ...
55 views

### What kind of transformation does the Y-gate do on the bloch sphere?

I'm going through "Quantum Computation & Quantum Information" by Michael A. Nielsen and Isaac L. Chuang, and as a high school student with no previous knowledge, I cannot understand some things ...
113 views

### Nielsen & Chuang Exercise 4.34 “Measuring an operator”

I need help with the exercise 4.34 from Nielsen & Chuang Book. I am supposed to get a matrix corresponding to the circuit. Thanks
135 views

### How to implement the exponential of an outer product?

In exercise 6.7 page 258 in Nielsen and Chuang book, they have a Hamiltonian $H = \left| x \right\rangle \!\!\left\langle x \right| + \left| \psi \right\rangle \!\!\left\langle \psi \right|$ and the ...
49 views

101 views

### Question Regarding Quantum Period-Finding Fourier Transform Approximation

I am following the 5.4.1 Period-Finding Algorithm in Nielsen and Chuang as shown below: My confusion lies with the second expression of point 3 in the procedure. Why is the second expression an ...