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Published May 2018 | Published + Submitted
Journal Article Open

Representation and design of wavelets using unitary circuits

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.

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.

Attached Files

Published - PhysRevA.97.052314.pdf

Submitted - 1605.07312v1.pdf

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Created:
August 19, 2023
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