Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909645714489344 |
|---|---|
| author | Markowitz, Matthew Miri, Mohammad-Ali Ovchinnikov, Alexey Zelaya, Kevin |
| author_facet | Markowitz, Matthew Miri, Mohammad-Ali Ovchinnikov, Alexey Zelaya, Kevin |
| contents | Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U(N)$ can be decomposed into a sequence of $N$-parameter phases alternating with $1$-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U(N)$ for a finite number of layers, which is numerically found to be exactly $N$. This architecture can be implemented using elementary optical components and can successfully reconstruct arbitrary unitary matrices. We propose example devices such as optical logic gates, which perform logic gate operations using a single-layer lossless and passive optical circuit design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries Markowitz, Matthew Miri, Mohammad-Ali Ovchinnikov, Alexey Zelaya, Kevin Quantum Physics Mathematical Physics Optics Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U(N)$ can be decomposed into a sequence of $N$-parameter phases alternating with $1$-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U(N)$ for a finite number of layers, which is numerically found to be exactly $N$. This architecture can be implemented using elementary optical components and can successfully reconstruct arbitrary unitary matrices. We propose example devices such as optical logic gates, which perform logic gate operations using a single-layer lossless and passive optical circuit design. |
| title | Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries |
| topic | Quantum Physics Mathematical Physics Optics |
| url | https://arxiv.org/abs/2506.08454 |