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. doi:10.1103/PhysRevA.97.052314. https://resolver.caltech.edu/CaltechAUTHORS:20161031-090659507
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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.
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| 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: | Institute for Quantum Information and Matter | |||||||||
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| Issue or Number: | 5 | |||||||||
| Classification Code: | PACS numbers: 05.30.-d, 02.70.-c, 03.67.Mn, 75.10.Jm | |||||||||
| DOI: | 10.1103/PhysRevA.97.052314 | |||||||||
| Record Number: | CaltechAUTHORS:20161031-090659507 | |||||||||
| Persistent URL: | https://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: | 11 Nov 2021 04:48 |
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