chapter-apps.tex

```
\chapter{Built-in Quantum Applications}\label{ch:apps}
This section describes the apps provided with this software, in the `Algorithms/' directory.
\begin{enumerate}
\item Cat-State Preparation: Prepares an $n$-bit quantum register in the maximally entangled Cat-State.
The app is parameterized by $n$.
\item Quantum Fourier Transform (QFT): Performs quantum Fourier transform on an $n$-bit
number. The app is parameterized by $n$.
\item Square Root: Uses a quantum concept
called \emph{amplitude amplification} to find the square root of an $n$-bit number
with the Grover's search technique\cite{Grover}. The app is parameterized by $n$.
\item Binary Welded Tree: Uses quantum random walk algorithm to
find a path between an entry and exit node of a binary welded tree
\cite{ref:bwt}. The app is parameterized by the height of the tree ($n$) and
a time parameter ($s$) within which to find the solution.
\item Ground State Estimation: Uses quantum phase estimation algorithm to
estimate the ground state energy of a molecule \cite{ref:gse}. The app
is parameterized by the size of the molecule in terms of its molecular
weight (M).
\item Triangle Finding Problem: Finds a triangle within a dense,
undirected graph \cite{ref:tfp}. The app is parameterized by the
number of nodes $n$ in the graph.
\item Boolean Formula: Uses the quantum algorithm described
in~\cite{ref:boolean_formula}, to compute a winning strategy for the game of
Hex. The app is parameterized by size of the Hex board $(x,y)$.
\item Class Number: A problem from computational algebraic number theory,
to compute the class group of a real quadratic number field
\cite{DBLP:conf/stoc/Hallgren05}. The app is parameterized by $p$, the
number of digits after the radix point for floating point numbers used in
computation.
\item Secure Hash Algorithm 1: An implementation of the reverse cryptographic hash function \cite{ref:sha1}. The message is decrypted by using the SHA-1 function as the oracle in a Grovers search algorithm. The app is parameterized by the size of the message in bits ($n$).
\item Shor's Factoring Algorithm: Performs factorization using the Quantum
Fourier Transform \cite{Shor}. The app is parameterized by $n$, the
size in bits of the number to factor.
\end{enumerate}
```