Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916309224128512 |
|---|---|
| author | Jin, Shi Liu, Nana |
| author_facet | Jin, Shi Liu, Nana |
| contents | We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-Scholes and Fokker-Planck equations. The key idea is to approximate the heat equations by a system of hyperbolic heat equations that involve only first-order differential operators. This scheme requires relatively simple interaction terms in the Hamiltonian, which are the electric and magnetic dipole moment-like interaction terms that would be present in a Jaynes-Cummings-like model. For a d-dimensional problem, we show that it is much more appropriate to use a single d-level quantum system - a qudit - instead of its qubit counterpart, and d+1 qumodes. The total resource cost is efficient in d and precision error, and has potential for realisability for instance in cavity and circuit QED systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models Jin, Shi Liu, Nana Quantum Physics Mathematical Physics We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-Scholes and Fokker-Planck equations. The key idea is to approximate the heat equations by a system of hyperbolic heat equations that involve only first-order differential operators. This scheme requires relatively simple interaction terms in the Hamiltonian, which are the electric and magnetic dipole moment-like interaction terms that would be present in a Jaynes-Cummings-like model. For a d-dimensional problem, we show that it is much more appropriate to use a single d-level quantum system - a qudit - instead of its qubit counterpart, and d+1 qumodes. The total resource cost is efficient in d and precision error, and has potential for realisability for instance in cavity and circuit QED systems. |
| title | Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2407.01913 |