Nové numerické metody pro kvantové řízení
| Název práce v češtině: | Nové numerické metody pro kvantové řízení |
|---|---|
| Název v anglickém jazyce: | New numerical methods for quantum control |
| Akademický rok vypsání: | 2025/2026 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Katedra numerické matematiky (32-KNM) |
| Vedoucí / školitel: | Stefano Pozza, Dr., Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 20.10.2025 |
| Datum zadání: | 20.10.2025 |
| Datum potvrzení stud. oddělením: | 20.10.2025 |
| Zásady pro vypracování |
| The thesis work requires the use and adaptation of innovative codes for spin dynamics simulations. The main task will be to integrate these codes with well-established optimization algorithms and to test them on applications in quantum computing and nuclear magnetic resonance. MATLAB will serve as the primary programming language. The project will also require a literature review of the relevant topics.
This project offers opportunities for collaboration with international partners from the *-Lanczos (www.starlanczos.cz) and the MAGICA project (https://anr.fr/Project-ANR-20-CE29-0007). Within the Erasmus+ framework, it may also be possible to arrange a research visit to one of the partner universities (Sorbonne, ULCO-Calais, or Pisa). |
| Seznam odborné literatury |
| - D'Alessandro, D. (2007). Introduction to Quantum Control and Dynamics (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781584888833
- Glaser, S., Boscain, U., Calarco, T. et al. Training Schrödinger’s cat: quantum optimal control. Eur. Phys. J. D 69, 279 (2015). https://doi.org/10.1140/epjd/e2015-60464-1 - Kuprov, I. (2023), Spin: From Basic Symmetries to Quantum Optimal Control. Springer Nature. - Pozza, S., Van Buggenhout, N. A ⋆-product solver with spectral accuracy for non-autonomous ordinary differential equations, Proceedings in Applied Mathematics & Mechanics, (2023). - Pozza, S., Van Buggenhout, A new Legendre polynomial-based approach for non-autonomous linear ODEs, Electron. Trans. Numer. Anal., 60, 292 (2024). https://doi.org/10.1553/etna_vol60s292 |
| Předběžná náplň práce |
| Quantum control seeks to manipulate atomic- and molecular-scale dynamics using external electromagnetic fields. Achieving this efficiently requires numerical simulations combined with optimization algorithms capable of identifying the parameters that best control the dynamics.
This work introduces a new approach to optimal control in quantum dynamics based on the so-called *-product. The method offers a novel way to express solutions of certain Schrödinger equations, potentially enabling faster computations and the design of more effective external field pulses. Applications will be explored in both quantum computing and nuclear magnetic resonance. |
| Předběžná náplň práce v anglickém jazyce |
| Quantum control seeks to manipulate atomic- and molecular-scale dynamics using external electromagnetic fields. Achieving this efficiently requires numerical simulations combined with optimization algorithms capable of identifying the parameters that best control the dynamics.
This work introduces a new approach to optimal control in quantum dynamics based on the so-called *-product. The method offers a novel way to express solutions of certain Schrödinger equations, potentially enabling faster computations and the design of more effective external field pulses. Applications will be explored in both quantum computing and nuclear magnetic resonance. |