  In this thesis we investigate two new Amplified Quantum Transforms. In
particular we create and analyze the Amplified Quantum Fourier Transform
(Amplified-QFT) and the Amplified-Haar Wavelet Transform. First, we provide a
brief history of quantum mechanics and quantum computing. Second, we examine
the Amplified-QFT in detail and compare it against the Quantum Fourier
Transform (QFT) and Quantum Hidden Subgroup (QHS) algorithms for solving the
Local Period Problem. We calculate the probabilities of success of each
algorithm and show the Amplified-QFT is quadratically faster than the QFT and
QHS algorithms. Third, we examine the Amplified-QFT algorithm for solving The
Local Period Problem with an Error Stream. Fourth, we produce an uncertainty
relation for the Amplified-QFT algorithm. Fifth, we show how the Amplified-Haar
Wavelet Transform can solve the Local Constant or Balanced Signal Decision
Problem which is a generalization of the Deutsch-Jozsa algorithm.
