Saved in:
| Main Authors: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.01455 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915964920004608 |
|---|---|
| author | Bleiler, Steven Chen, Shanyan O'Neil, Emma Reich, J. Eliot Rezvani, Julia Whitham-Powell, Elijah Al-Bayaty, Ali Jegier, Jerzy Yang, Sonia Perkowski, Marek |
| author_facet | Bleiler, Steven Chen, Shanyan O'Neil, Emma Reich, J. Eliot Rezvani, Julia Whitham-Powell, Elijah Al-Bayaty, Ali Jegier, Jerzy Yang, Sonia Perkowski, Marek |
| contents | We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of the toric geometric structure of the state space. Visualizations of these state spaces and of certain fundamental unitary transformations in binary and ternary quantum logic and a method to develop new transformations based on these visualization techniques are presented. Transformations discussed included minimal universal sets for permutative ternary quantum circuits. In addition, general structures and synthesis methods based on quantum multiplexers are presented. A general framework for the design of optimal ternary quantum transformations and circuits is additionally presented. Finally, a number of open research areas that are extensions of the work presented herein are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Visualizing the state space and transformations of higher order quantum logics via toric geometry Bleiler, Steven Chen, Shanyan O'Neil, Emma Reich, J. Eliot Rezvani, Julia Whitham-Powell, Elijah Al-Bayaty, Ali Jegier, Jerzy Yang, Sonia Perkowski, Marek Quantum Physics Algebraic Geometry We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of the toric geometric structure of the state space. Visualizations of these state spaces and of certain fundamental unitary transformations in binary and ternary quantum logic and a method to develop new transformations based on these visualization techniques are presented. Transformations discussed included minimal universal sets for permutative ternary quantum circuits. In addition, general structures and synthesis methods based on quantum multiplexers are presented. A general framework for the design of optimal ternary quantum transformations and circuits is additionally presented. Finally, a number of open research areas that are extensions of the work presented herein are given. |
| title | Visualizing the state space and transformations of higher order quantum logics via toric geometry |
| topic | Quantum Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2510.01455 |