Adiabatické a variační metody

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra počítačů

Anotace:

Požadavky:

Osnova přednášek:

1.A view from physical chemistry (energy levels of molecules) vs. a view from theoretical computer science (MAXCUT)

2.EQA Conjecture

3.Inapproximability and the unique games conjecture

4.Adiabatic theorem and quantum speedup by quantum annealing (QA)

5.Variational quantum eigensolver (VQE)

6.Quantum Approximate Optimization Algorithm (QAOA)

7.Parameter shift rule (PSR)

8.Iteration complexity of QAOA with PSR

9.Per-iteration complexity of QAOA

10.Warm-starting quantum optimization: rounded

11.Warm-starting quantum optimization: continuous-valued

12.Applications: variational solvers for systems of linear equations.

13.Applications: variational solvers for Markowitz portfolio management.

Osnova cvičení:

1.Background: MAXCUT

2.Background: SDP

3.Background: Goemans-Williamson Hyperplane Rounding

4.Variational quantum eigensolver (VQE)

5.Quantum Approximate Optimization Algorithm (QAOA)

6.Parameter shift rule (PSR)

7.Experimenting with iteration complexity of QAOA with PSR

8.Experimenting with depth of circuits in QAOA

9.Warm-starting quantum optimization: rounded

10.Warm-starting quantum optimization: continuous-valued

11.1:1 advice on individual projects.

12.1:1 advice on individual projects.

Cíle studia:

Studijní materiály:

Amira Abbas, Andris Ambainis, ..., J. Mareček, et al.: Quantum optimization: Potential, challenges, and the path forward. arXiv preprint arXiv:2312.02279. (Lectures 1 and 2.)

RD Somma, D Nagaj, M Kieferová: Quantum speedup by quantum annealing. Physical review letters 109 (5), 050501 (2012). https://arxiv.org/abs/1202.6257 (Lecture 4)

Daniel J. Egger, Jakub Marecek, Stefan Woerner: Warm-starting quantum optimization. Quantum 5, 479 (2021). https://arxiv.org/abs/2009.10095 (Lectures 10, 11, 13)

Lennart Bittel, Martin Kliesch: Training variational quantum algorithms is NP-Hard. Physical review letters 127, 120502 (2021). https://arxiv.org/abs/2101.07267 (Lecture 9)

Ruizhe Zhang, Guoming Wang, and Peter Johnson: Computing Ground State Properties with Early Fault Tolerant Quantum Computers. Quantum 6, 761 (2022). https://arxiv.org/abs/2109.13957v2 (Lectures 1 and 2.)

Vyacheslav Kungurtsev, Georgios Korpas, Jakub Marecek, Elton Yechao Zhu: Iteration Complexity of Variational Quantum Algorithms. Quantum (2024). https://arxiv.org/abs/2209.10615 (Lecture 8)

Reference works:

Kristály A, Rădulescu V, Varga C, Variational Principles in Mathematical Physics, Geometry, and Economics, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, UK, 2010. ISBN-10: 0521117828 | ISBN-13: 9780521117821

(Lecture 1)

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