Abstract
Wavelets with great filter length, also known as high-order wavelets, exhibit favorable properties and superior performance in classical signal processing. We study the performance of great-length wavelets in the quantum computation of a dynamical model. Numerical results indicate that certain classical properties of wavelets can significantly improve their quantum localization capability. In particular, smooth wavelets have a quantum localization capability up to 10 times stronger than non-smooth ones, as measured by the Inverse Participation Ratio (IPR).Also, we propose an efficient quantum algorithm for approximating wavelets of any length m in time Opoly(logN,log1ϵ,m), achieving a poly-logarithmic dependence on the inverse of precision 1ϵ and the system dimension N. We show analytically and numerically that the quantum wavelet-based denoising algorithm succeeds with a constant probability, independent of the dimension N.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
