Cleve, Richard E.Ahokas, Graeme Robert2005-08-162005-08-162004Ahokas, G. R. (2004). Improved algorithms for approximate quantum fourier transforms and sparse hamiltonian simulations (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/228390612933458http://hdl.handle.net/1880/41417Bibliography: p. 104-107We investigate and improve algorithms for computing the approximate quantum Fourier transform (QFT ) and simulating a sparse Hamiltonian. We present an improved near-linear time algorithm for the approximate QFT modulo 2™. We give a circuit for the arbitrary modulus version that matches the best currently-known bound. We then relate the difficulty of the arbitrary modulus QFT to classical integer multiplication and division. We also investigate the problem of simulating an n-qubit sparse Hamiltonian. As input we receive the system's start state, a black box which, via queries, provides the non-zero entries of each row of the Hamiltonian, and a time t. We present an improved polynomial-time quantum algorithm for computing an approximation of the state of the system at time t. Prior to this, we provide an introduction to quantum computing, and survey some quantum algorithms that are used in our improved algorithms.viii, 114 leaves : ill. ; 30 cm.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.master thesis10.11575/PRISM/22839AC1 .T484 2004 A46