Simple Quantum Coins Enable Pretty Good State Transfer on Every Hypercube
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916545846837248 |
|---|---|
| author | Zhan, Hanmeng |
| author_facet | Zhan, Hanmeng |
| contents | We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube $Q_d$. When $d$ is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every $Q_d$. Our coins are real, and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple Quantum Coins Enable Pretty Good State Transfer on Every Hypercube Zhan, Hanmeng Combinatorics Discrete Mathematics Quantum Physics We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube $Q_d$. When $d$ is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every $Q_d$. Our coins are real, and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs. |
| title | Simple Quantum Coins Enable Pretty Good State Transfer on Every Hypercube |
| topic | Combinatorics Discrete Mathematics Quantum Physics |
| url | https://arxiv.org/abs/2412.20753 |