Chap 5 Q Fourier Transform: p 216-247 Avery Leider The information presented here, although greatly condensed, comes almost entirely from the course textbook: Quantum Computation and Quantum Information by Nielsen & Chuang and the tutorials written by Prof Ronald Frank

5.1 Why the investment in Quantum Computing? Prime factorization of an n-bit integer on a classical computer using the number field sieve: Same task with a quantum algorithm: Quantum is faster!

Military Applications Quantum Computing

5.1 Quantum Fourier Transform Quantum Fourier Transform is an algorithm used in quantum factoring of primes, and other quantum algorithms. Useful for warfare. Quantum Computing

Fourier series illustration by Pierre Guilleminot https://bl.ocks.org/jinroh/7524988 Research Seminar 1 Review

5.1 Quantum Fourier Transform From Box 5.1 on page 220 of Nielsen, M.A. and Chuang, I., 2002. Quantum computation and quantum information. Quantum Computing

5.2 Quantum Phase Estimation algorithm Phase Estimation uses the inverse Quantum Fourier transform Phase Estimation makes it possible to estimate the phase that a unitary transformation adds to one of its eigenvectors.

Quantum Phase Estimation Phase Estimation is a subroutine that prepares an eigenstate of the Hermitian operator in one register It stores the corresponding eigenvalue in a 2nd register It uses momentum and phase shifts & inverse Quantum Fourier transform https://quantumexperience.ng.bluemix.net/proxy/tutorial/full-user-guide/004-Quantum_Algorithms/100-Quantum_Phase_Estimation.html Quantum Computing

Phase Estimation Quantum Computing

Research Seminar 1 Review Phase Estimation Research Seminar 1 Review

Research Seminar 1 Review Phase Estimation Phase Estimation, combined with quantum search algorithm, can solve the problem of counting solutions to a search problem. Phase Estimation supports solutions to the order-finding problem and the factoring problem. Research Seminar 1 Review

5.4 General Applications of the quantum Fourier transform Period finding Discrete logarithms Hidden subgroup problem Other quantum algorithms? Quantum Computing

5.4 General Applications of the quantum Fourier transform Quantum Computing can solve some problems exponentially better than classical computers. Other problems it is polynominally better. Quantum Fourier Transform is involved in most of these advantages But in some cases, it is not any better. Quantum Computing