Add JB as contributor, refactor structure of part of books

Author: Scinawa

appendix.Rmd

@@ -4,6 +4,7 @@ output:
   html_document: default
 ---
 
+# (PART) Part (appendix) {-} 
 
 # (APPENDIX) Appendix {-} 
 
@@ -112,13 +113,13 @@ Bound $\|A^TA - \overline{A}^T\overline{A}\|_F$
 
 
 
-```{definition, name="Distance"}
+```{definition, distance, name="Distance"}
 A function $f : \mathbb{R}^d \times \mathbb{R}^d \mapsto \mathbb{R}$ is called a distance if:
 
 - $d(x,y) \geq 0$
 - $d(x,y) = 0$ iif $x=y$
 - $d(x,y)=d(y,x)$
-- $d(x,z) \leq d(x,y) + d(x,y+z)$
+- $d(x,z) \leq d(x,y) + d(y,z)$
 
 ```
 
@@ -380,8 +381,8 @@ Another interesting result about the SVD of a matrix is known as the Eckart–Yo
 ```{theorem, eckart-young-mirsky, name="Best F-Norm Low Rank Approximation"}
  \cite{eckart1936approximation}\cite{mirsky1960symmetric} \label{Theo:eckart-young-mirsky}
 Let $A  \in \mathbb{R}^{n \times m}$ be a matrix of rank $r$ and singular value decomposition $A  = U \Sigma V ^T$. The matrix $A ^{(k)} = U ^{(k)}\Sigma ^{(k)}V ^{(k)T}$ of rank $k \leq r$, obtained by zeroing the smallest $r-k$ singular values of $A$, is the best rank-k approximation of $A$.
- Equivalently, $A _k = argmin_{B :rank(B )=k}(||A  - B  ||_F)$.
- Furthermore, $min_{B :rank(B )=k}(||A  - B  ||_F) = \sqrt{\sum_{i=k+1}^r{\sigma_i}}$.
+ Equivalently, $A _k = argmin_{B :rank(B )=k}(\|A  - B  \|_F)$.
+ Furthermore, $min_{B :rank(B )=k}(\|A  - B  \|_F) = \sqrt{\sum_{i=k+1}^r{\sigma_i}}$.
 ```
 
 
@@ -1198,15 +1199,20 @@ If you want to give me any feedback, feel free to write me at "scinawa - at - lu
 In sparse order, I would like to thank [Dong Ping Zhang](www.dongpingzhang.com), [Mehdi Mhalla](http://membres-lig.imag.fr/mhalla/) , [Simon Perdrix](https://members.loria.fr/SPerdrix/), [Tommaso Fontana](https://twitter.com/zommiommy), and [Nicola](https://www.linkedin.com/in/nvitucci/) [Vitucci](https://twitter.com/nvitucci) for the initial help with the previous version of this project, and the helpful words of encouragement.
 
 
-The [contributors](https://github.com/Scinawa/quantumalgorithms.org/graphs/contributors) to the project are:
+
+**Core team**
 
 - Alessandro ['Scinawa'](https://twitter.com/scinawa) Luongo
 - Armando ['ikiga1'](https://twitter.com/ikiga1) Bellante
+
+The [contributors](https://github.com/Scinawa/quantumalgorithms.org/graphs/contributors) to the project are:
+
 - Patrick Rebentrost
 - Yassine Hamoudi
 - Martin Plávala
 - Trong Duong
 - Filippo Miatto
+- Jinge Bao
 
 # License and citation
 

index.Rmd

@@ -1,6 +1,6 @@
 --- 
 title: "Quantum algorithms for data analysis"
-author: ""
+author: "Alessandro Luongo"
 date: "`r Sys.Date()`"
 site: bookdown::bookdown_site
 documentclass: book
@@ -117,7 +117,7 @@ https://stackoverflow.com/questions/41084020/add-a-html-block-above-each-chapter
 - March 2021: quantumalgorithms.org is proudly supported by the [Unitary Fund](https://unitary.fund/), and quantumalgorithms.org is a project of the [QOSF](https://qosf.org) mentorship program: 5 students started creating new content!
 - April 2021: Mobile version working, search functionality added, q-means, finding the minimum, new algo for dimensionality reduction, and factor score ratio estimation estimation. 
 
-Arriving soon:
+Coming soon:
 
 - quantum perceptrons
 - quantum lower bounds

toolbox.Rmd

@@ -15,6 +15,11 @@ We now want to show an algorithm that finds the minimum among $N$ unsorted value
 Given quantum access to a vector $u \in [0,1]^N$ via the operation $\ket j \ket{\bar 0} \to \ket j \ket{ u_j}$ on $\Ord{\log N}$ qubits, where $u_j$ is encoded to additive accuracy $\Ord{1/N}$. Then, we can find the minimum $u_{\min} = \min_{j\in[N]}  u_j$ with success probability $1-\delta$ with $\Ord{\sqrt N \log \left (\frac{1}{\delta}\right) }$ queries and $\tOrd{\sqrt N  \log \left( \frac{1}{\delta}\right )}$ quantum gates.
 ```
 
+Another formulation is the following: 
+```{theorem, finding-minimum-2, name="Quantum Minimum Finding [@durr1996quantum] formulation of [@ambainis2019quantum]"}
+Let $a_1, \ldots, a_n$ be integers, accessed by a procedure $\mathcal P$.
+There exists a quantum algorithm that finds $\min_{i=1}^n \{a_i\}$ with success probability at least $2/3$ using $O(\sqrt n)$ applications of $\mathcal P$.
+```