CaltechAUTHORS
  A Caltech Library Service

Representation and design of wavelets using unitary circuits

Evenbly, Glen and White, Steven R. (2018) Representation and design of wavelets using unitary circuits. Physical Review A, 97 (5). Art. No. 052314. ISSN 2469-9926. http://resolver.caltech.edu/CaltechAUTHORS:20161031-090659507

[img] PDF - Published Version
See Usage Policy.

3827Kb
[img] PDF - Submitted Version
See Usage Policy.

2154Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20161031-090659507

Abstract

The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.97.052314DOIArticle
https://arxiv.org/abs/1605.07312arXivDiscussion Paper
Additional Information:© 2018 American Physical Society. Received 20 September 2017; published 11 May 2018. The authors acknowledge support by the Simons Foundation (Many Electron Collaboration). S.R.W. acknowledges funding from the NSF under Grant No. DMR-1505406.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
NSFDMR-1505406
Classification Code:PACS numbers: 05.30.-d, 02.70.-c, 03.67.Mn, 75.10.Jm
Record Number:CaltechAUTHORS:20161031-090659507
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161031-090659507
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71608
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Oct 2016 17:18
Last Modified:16 Nov 2018 23:46

Repository Staff Only: item control page