Generation of Novel Wavelet Transformations towards applications in Tensor Network Algorithms
| dc.contributor.author | Dayton, Aaron | |
| dc.date.accessioned | 2024-03-17T04:27:36Z | |
| dc.date.available | 2024-03-17T04:27:36Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | Wavelets can be formulated in a pyramidal gate structure of unitary rotation matrices which satisfy a set of vanishing moment equations. The vanishing moment equations can be satisfied by passing them into a cost function and minimizing with the Nelder-Mead algorithm. Barren plateau-like features exist in the solution-space of the vanishing moment equations which make it difficult to solve for greater circuit depths. The basins of these barren plateaus can be widened by introducing a parameter, β, in the exponent of each vanishing moment equation for a given circuit. Wavelets up to depth 3, β=1, are generated to high precision and shown to match the known Daubechies wavelets. Solutions to the altered vanishing moment equations are shown to exist on a continuum for a domain of β-values for the depth 2 circuit. An improved algorithm for solving for wavelet circuits of greater depths is proposed. These wavelets will be used in the multi-scale entanglement renormalization ansatz (MERA) tensor network algorithm to solve for the ground state energy of gapless systems. | |
| dc.description.reviewstatus | Reviewed | |
| dc.description.scholarlevel | Undergraduate | |
| dc.description.sponsorship | Jamie Cassels Undergraduate Research Awards (JCURA) | |
| dc.identifier.uri | https://hdl.handle.net/1828/16211 | |
| dc.language.iso | en | |
| dc.publisher | University of Victoria | |
| dc.subject | Wavelet | |
| dc.subject | Tensor-Network | |
| dc.subject | quantum | |
| dc.subject | algorithm | |
| dc.subject | MERA | |
| dc.subject | Gapless-System | |
| dc.title | Generation of Novel Wavelet Transformations towards applications in Tensor Network Algorithms | |
| dc.type | Poster |