1 / 13

Chap 5 Q Fourier Transform : p 216-247

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.

aliciaward
Download Presentation

Chap 5 Q Fourier Transform : p 216-247

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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!

  3. Military Applications Quantum Computing

  4. 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

  5. Fourier seriesillustration by Pierre Guilleminot • https://bl.ocks.org/jinroh/7524988 Research Seminar 1 Review

  6. 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

  7. 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.

  8. 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

  9. Phase Estimation Quantum Computing

  10. Phase Estimation Research Seminar 1 Review

  11. 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

  12. 5.4 General Applications of the quantum Fourier transform • Period finding • Discrete logarithms • Hidden subgroup problem • Other quantum algorithms? Quantum Computing

  13. 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

More Related