Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910675574456320 |
|---|---|
| author | Lewis, Dylan Eidenbenz, Stephan Nadiga, Balasubramanya Subaşı, Yiğit |
| author_facet | Lewis, Dylan Eidenbenz, Stephan Nadiga, Balasubramanya Subaşı, Yiğit |
| contents | We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of their open questions. We provide a further significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector. Given a natural choice of coordinates for a dynamical system with one or more positive Lyapunov exponents and solutions that grow sub-exponentially, we prove that any such algorithm has complexity scaling at least exponentially in the integration time. As such, an efficient quantum algorithm for simulating chaotic systems or regimes is likely not possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09593 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems Lewis, Dylan Eidenbenz, Stephan Nadiga, Balasubramanya Subaşı, Yiğit Quantum Physics We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of their open questions. We provide a further significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector. Given a natural choice of coordinates for a dynamical system with one or more positive Lyapunov exponents and solutions that grow sub-exponentially, we prove that any such algorithm has complexity scaling at least exponentially in the integration time. As such, an efficient quantum algorithm for simulating chaotic systems or regimes is likely not possible. |
| title | Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.09593 |