\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}