Annotation
Understanding quantum many-body systems is one of the main challenges in both condensed matter physics and quantum computing. The difficulty comes from the exponential growth of the Hilbert space, which quickly makes these problems hard to handle, both classically and on quantum devices. Many of these systems have symmetries, but their role in quantum algorithms is often not fully applied. As a results, quantum algorithms may explore large parts of the Hilbert space that are not physically relevant.
In this talk, it will be discussed how symmetries can be used in a more practical way when designing quantum algorithms. Spin models will be used as examples where the role of symmetry can be clearly seen. In these systems, symmetry constraints reduce the effective size of Hilbert space, increase spectral gaps, and help the algorithms focus on the physically relevant part of the problem. This leads to a more stable and efficient behavior of the algorithms such as variational quantum algorithm (VQE), quantum phase estimation (QPE) and its iterative version (IQPE).
Benefits for the attendees, what they will learn:
The seminar will provide an overview of how symmetries can be used in quantum algorithms for many- body systems. Participants will gain an understanding of how symmetry constraints and projection techniques can improve quantum state preparation, optimisation in variational algorithms, and the performance of phase estimation methods. The talk will also offer a practical perspective on how these ideas can be incorporated into existing quantum algorithms.
Level
Beginner - intermediate
Language
English
Prerequisites
Basic knowledge of quantum mechanics and linear algebra is helpful, but not strictly required.
Tutor
Ivana Miháliková is a postdoctoral researcher in the Quantum Computing laboratory at the IT4Innovations National Supercomputer Center and is also affiliated with the Institute of Physics of the Slovak Academy of Sciences and Matej Bel University. She received her Ph.D. in condensed matter physics from Masaryk University, where her research focused on the application of quantum computing methods in theoretical materials science. During her Ph.D., she was awarded the Quantum Computing Fellowship at Los Alamos National Laboratory and participated in international projects and conferences. Her current research focuses on benchmarking quantum computers and the preparation of thermal states.
Acknowledgements
This course was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ (ID:90254).
All presentations and educational materials of this course are provided under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license.