Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913203693289472 |
|---|---|
| author | Ogunkoya, Oluwadara Kim, Joonho Peng, Bo Özgüler, A. Barış Alexeev, Yuri |
| author_facet | Ogunkoya, Oluwadara Kim, Joonho Peng, Bo Özgüler, A. Barış Alexeev, Yuri |
| contents | Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to $d$-dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, that may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our work outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00740 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation Ogunkoya, Oluwadara Kim, Joonho Peng, Bo Özgüler, A. Barış Alexeev, Yuri Quantum Physics Mathematical Physics Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to $d$-dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, that may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our work outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing. |
| title | Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2309.00740 |