Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.11579 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910305781547008 |
|---|---|
| author | Aifer, Maxwell Sheldon, Evan |
| author_facet | Aifer, Maxwell Sheldon, Evan |
| contents | Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute these logarithms using a quantum computer, assuming that the group addition operation can be computed efficiently on a quantum device. Currently, however, thousands of logical qubits are required for elliptic curve group addition, putting this application out of reach for near-term quantum hardware. Here we give an algorithm for computing elliptic curve group addition using a single continuous-variable mode, based on weak measurements of a system with a cubic potential energy. This result could lead to improvements in the efficiency of elliptic curve discrete logarithms using a quantum device. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11579 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elliptic Curves in Continuous-Variable Quantum Systems Aifer, Maxwell Sheldon, Evan Quantum Physics Mathematical Physics Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute these logarithms using a quantum computer, assuming that the group addition operation can be computed efficiently on a quantum device. Currently, however, thousands of logical qubits are required for elliptic curve group addition, putting this application out of reach for near-term quantum hardware. Here we give an algorithm for computing elliptic curve group addition using a single continuous-variable mode, based on weak measurements of a system with a cubic potential energy. This result could lead to improvements in the efficiency of elliptic curve discrete logarithms using a quantum device. |
| title | Elliptic Curves in Continuous-Variable Quantum Systems |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2401.11579 |