KAZHDAN's SUNDAY SEMINAR, 14:00-16:00, HEBREW UNIVERSITY
Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler
First lecture: 27 Oct 2019 Last lecture: 19 Jan 2020.
Syllabus:
1. Mathematical models of classical and quantum mechanics. (Leonid)
Lecture 1 (notes)
2. Correspondence principle and quantization. (Leonid)
Lecture 2 (notes) Lectures 1,2 (hand-written notes)
3. Classical and quantum computation: gates, circuits, algorithms. (Gil)
4. Quantum states, measurements and circuits. Solovay-Kitaev. (Dorit)
Lecture 4 (notes)
5. Time-energy uncertainty and quantum computation. Shor algorithm. (Dorit)
Lecture 5 (notes)
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy. (Leonid)
Lecture 6 (notes)
7. Noisy classical and quantum computing and error correction. Kitaev's surface code. (Guy)
Lecture 7 (hand-written notes)
8. Noise stability and noise sensitivity of Boolean functions, noisy boson sampling (Gil)
9. Threshold theorem- quantum fault tolerance (Dorit)
10. Quantum noise and measurement, and rigidity of the Poisson bracket (Leonid)
Lecture 10 (notes)
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
https://arxiv.org/abs/quant-ph/9812037
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
https://arxiv.org/abs/1801.02602
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
https://www.math.ias.edu/files/mathandcomp.pdf